OOTS #1277 - The Discussion Thread

[tanonx]

So here's my position: we know there is not going to be a group of people coming in to help the Order. Roy said they rang the alarm bell and nobody cared in Girard's pyramid, we saw the pirates ask why they should keep helping and saw the Order couldn't explain it even without any limitations on communication, and we saw all the High Priests who know exactly what is happening and what it means refuse to offer any help. All indications are that the Order is on their own.

Now, with this being the case, any claims of "but they could call for help" seem, to me, spurious at best. If you want to discuss a hypothetical scenario in which none of these indications happened and what would happen if they just Sent to a bunch of clerics they don't know and described the scenario perfectly and asked for help all within a 25 word limit and said clerics were both inclined and able to come, then i misunderstood and of course feel free to speculate away, i wont take part and i apologize for my misunderstanding and for butting in.

But if the position is "they can still call for help with current canon as-is" then im going to point out where it fails (because it will fail) and not bother with the rest.

The problem here is, "the rest" breaks down why these examples are wrong. They're a longer, more detailed version of something like this:

• Belkar was the one who claimed the alarm was rung when Azure City got destroyed, after Roy was the one considering calling for help. Specifically needling him back into action, not delivering 9 WIS revelations, given this was well before they even learned the full extent of the situation at the Godsmoot, let alone told anyone. It's not actually possible for them to have done so at that point.
• The Order did not explain anything to the pirate crew, because paying them was quicker and easier. Nothing says they can't negotiate with anyone else they contact, either.
• I just finished explaining that the only High Priest who could speed their way to their destination, and guarantee meaningful assistance from their clergy, immediately did so. And when they got to the temple, that rune set them up with free reign on the potion stash, and the help of every able fighter in the organization... which was just Minrah, because it turns out the rest of the clergy already died fighting the forces of Hel.

Meaning your position is based on something that's tangibly not the case in the world of the comic. But naturally it's not too helpful to throw comic links where you don't want them.

If you don't want to bother with the rest, then I think it'd be me who needs to apologize, and butt out of the hypothetical. I mostly just read the comics, so maybe I'm just not up to speed?

[Sebastian]

Excellent. Perfectly logical, and yet I have to admit I would have never guessed it. Congratulation to the Giant.

[Peelee]

The problem here is, "the rest" breaks down why these examples are wrong. They're a longer, more detailed version of something like this:

• Belkar was the one who claimed the alarm was rung when Azure City got destroyed, after Roy was the one considering calling for help. Specifically needling him back into action, not delivering 9 WIS revelations, given this was well before they even learned the full extent of the situation at the Godsmoot, let alone told anyone. It's not actually possible for them to have done so at that

Roy, who in the context of the scene is emotionally compromised and distraught and in full-blown denial, thinks of something. Belkar, who is the voice of reason in this scene, as he has been before, shoots it down, and everyone accepts his answer without rebuttal.

• The Order did not explain anything to the pirate crew, because paying them was quicker and easier. Nothing says they can't negotiate with anyone else they contact, either.

The Order tried (and were unable) to figure out how to do it, which then led to them just paying. After all, they want help with an apocalypse, but this universe has so many "world-ending" quests that the pirates even phrased it "apocalypse-of-the-week". And it's doubtful that they even know of every single world-ending quest to start with. Or, if you like, it's a boy-who-cried-wolf scenario and this time the world really is ending but everyone has heard it so much that nobody believes it anymore.

Either way, the overall point for these two scenes is that absent an editorial textblock where the author speaks directly to the audience, the only way he has to get information to us is through characters. These are both examples of the author pre-emptively answering audience questions of "but why can't the Order just get help from others?" Because they're not going to, and the author has told us as much at least twice now, and if they ever come into being validly of recruiting actual help and not just transportation, for example, something will happen making it impossible (eg the high priests being cloistered until the whole thing is done anyway).

• I just finished explaining that the only High Priest who could speed their way to their destination, and guarantee meaningful assistance from their clergy, immediately did so.

Except that high priest offered no assistance for the world ending quest. She offered assistance for the dwarf lands, which are under attack and she wants to protect because she's from there. It's like if someone said "the people ransacking this house are going to overthrow the government" and I said "Oh no! My house! Well, here's the key to the front door, please get them out of there."

Again, at the end of the day, the author's only way to convey information to us is via characters. The characters have told us at least twice that the Order is pretty much on their own here. If you wash to keep engaging in the idea that no, it's still possible despite the abundance of information saying it is not, then I don't think anything else i can say will change your mind).

[Satohika]

Thank you Mr. Burlew. I like Serini's funny speech patterns.

[Laurentio III]

To be fair, the titular panties were a relatively minor subplot in the overall story of the book. They were only relevant because it was set up in a previous book as an Impossible Question. Most of the time she runs around naked anyway, because she's a mermaid.

Plus, it Xanth-verse, female panties have inherent magical powers. So, it's probably a reasonable question anyway.
(I didn't read it, too. I stopped around the 12th or such book, when half the plot is a pretext for rapid-fire bad puns. Do they became better later?)

[dancrilis]

Did you skip this:

No I read that - I also felt I covered that (essentially yes that is true, it is also not relevant (at least to what I was saying).

It should be trivial to prove me wrong - you just need to give me a value from the bigger set that does not have a matching value in the smaller. Be aware, before you give me "2.3", that the matching value I will give you back is x = (y-1)/2 +1, where y is the number you give me (assuming we are sticking with s1 and s3*). So, for 2.3, I'll give you 1.65. So, knowing my "secret" of how I'll pair every number from what you claim is a bigger set, if you are right, there should still be infinitely many numbers I can't match to one in the smaller set. So, give me one.

If you can't, it's because they are the exact same size.

(BTW, this same approach is the one I like best to prove that 0.999... = 1; if they weren't the same number, you could give me any of the infinite numbers between them. But you can't, therefore they must be the same number. Infinities are weird that way)

Grey Wolf

*If you want, we could switch to s'1, the set of real numbers between 0 and 1, and s'3, the set of real numbers between 0 and 2. Then, the formula is the much simpler x' = y'/2

I get what you are saying (I believe) and you are not wrong - it is simply nothing to do with what I was saying.

Take a set1 {1,2,3} and a set2 {2,3,4} and a set3 {1,2,3,4} - you can assign numbers from the first set to the second 1 maps to 2, 2 to 3 and 3 to 4 - they have the same amount of data. you could extropolate this out to infinity and you would never encounter a number you couldn't match.
The third set has more data then either of the others and in fact you could express the third set as {set1, 4}.

If you express set1 as {set1} and set3 as {set1, 4} then you can determine that if you remove set1 from both that set1 would have nothing in it and set3 would have 4 in it.

This doesn't change simply because the individual sets have an infinite amount within them.

It is fair to say that if you could a set of infinite numbers the result will be infinite and if you count another set of infinite numbers the result will also be infinite - that does not mean that the two infinities are the same or that it cannot be shown that one of the infinities is larger then the other.

I entered this stating:

There are an infinite amount of numbers between 1 and 2, and there are also an infinite amount of numbers between 1 and 3.

That second infinity encompasses the first and also has extra - they are not the same size.

That remains a true statement - that you could choose any number between 1 and 3 and assign it a number between 1 and 2 does not mean that the range 1 to 3 does not encompass the range 1 to 2 and also have extra.

[Kish]

Plus, it Xanth-verse, female panties have inherent magical powers. So, it's probably a reasonable question anyway.
(I didn't read it, too. I stopped around the 12th or such book, when half the plot is a pretext for rapid-fire bad puns. Do they became better later?)

Well now, my understanding is that the ratio of puns continues to increase, but the number of rape and sexual assault references threatens to overtake them later. So...depends on what you consider "better."

[The MunchKING]

Well now, my understanding is that the ratio of puns continues to increase, but the number of rape and sexual assault references threatens to overtake them later. So...depends on what you consider "better."

That was a thing LONG before 15. Like literally the 5th book is all about that theme.

[Hopeless]

I'm going to have to reread this entire thread, but I wanted to ask a quick question before doing so.

Did they seriously need to check EVERY door and dungeon before the true dungeon was revealed?

Literally until every one was opened and checked before that would reveal the true dungeon where that Gate is hidden?!

If accurate oh wow and I thought it would reveal having dug up that gorge for those doors and linked dungeons we would learn the actual Gate was located above the clouds hidden from view.

So in a few issues we should witness that reveal!

The last door and dungeon checked should result in the true door to the dungeon where the Gate is hidden is revealed but wouldn't that mean the others would disappear and Xykon and Redcloaks allies might be a little angry if they lose their hunting grounds?

Now I better get back to reading!

[The MunchKING]

Did they seriously need to check EVERY door and dungeon before the true dungeon was revealed?

Literally until every one was opened and checked before that would reveal the true dungeon where that Gate is hidden?!

That's what they said in the comic. So barring a new plot-twist, yes.

The last door and dungeon checked should result in the true door to the dungeon where the Gate is hidden is revealed but wouldn't that mean the others would disappear and Xykon and Redcloaks allies might be a little angry if they lose their hunting grounds?

Now I better get back to reading!

Not necessarily. more likely is it just opens another door somewhere else rather than getting rid of all the existing doors. especially because if the trigger is at the back of each dungeon, getting rid of the doors would leave the people trying to get to the dungeon stuck inside, not able to get where they are going.

[dancrilis]

On consideration I think the next plan for the Order might be to check with Serini how sturdy the dungeons are - Xykon is not phasing through the walls or blasting through the walls or getting a chisel and chiseling through the walls at present, some of which might be to avoid damaging the gate but some of which may be that the walls are well made.

If the walls are sufficently well made then simply fully turning off the swap over in a dungeon he is in might trap him for a while (possible even a fairly long while) and buy a bit of time to consider things further.

[Grey_Wolf_c]

Take a set1 {1,2,3} and a set2 {2,3,4} and a set3 {1,2,3,4} - you can assign numbers from the first set to the second 1 maps to 2, 2 to 3 and 3 to 4 - they have the same amount of data. you could extropolate this out to infinity and you would never encounter a number you couldn't match.
The third set has more data then either of the others and in fact you could express the third set as {set1, 4}.

This doesn't change simply because the individual sets have an infinite amount within them.

I agree, it doesn't, but you are not obeying your own rules. I agree you can prove the last set is bigger because it has one item, {4} that cannot be mapped. So now, answer my challenge: what value in the original s3 or s'3 can't be matched to s1 or s'1? If you cannot find me the equivalent to the {4} in your latest example, then s1 and s3 are the equally big.

It is fair to say that if you could a set of infinite numbers the result will be infinite and if you count another set of infinite numbers the result will also be infinite - that does not mean that the two infinities are the same or that it cannot be shown that one of the infinities is larger then the other.

Certainly. The problem here is that your examples are NOT bigger infinities. They are the same sized infinity. If they were not, you could give me any one of the infinite numbers of s3 that were not matched 1-1 with s1. But I assume from the lack of any such examples in your post that you cannot in fact give me any, thus demonstrating that they are in fact equally big.

That remains a true statement - that you could choose any number between 1 and 3 and assign it a number between 1 and 2 does not mean that the range 1 to 3 does not encompass the range 1 to 2 and also have extra.

Incorrect. It means exactly that. Because you can map every number of s3 to every number in s1, it absolutely means they are the same size of infinity.

Again: you said it yourself: if you can map 1-1, then they are the same size. If you can't, if you have numbers left over such as {4}, then they are not the same size. So put up or accept you are wrong: what number in s3 can't be matched to s1?

Grey Wolf

[dancrilis]

I agree, it doesn't, but you are not obeying your own rules. I agree you can prove the last set is bigger because it has one item, {4} that cannot be mapped. So now, answer my challenge: what value in the original s3 or s'3 can't be matched to s1 or s'1? If you cannot find me the equivalent to the {4} in your latest example, then s1 and s3 are the equally big.


Certainly. The problem here is that your examples are NOT bigger infinities. They are the same sized infinity. If they were not, you could give me any one of the infinite numbers of s3 that were not matched 1-1 with s1. But I assume from the lack of any such examples in your post that you cannot in fact give me any, thus demonstrating that they are in fact equally big.



Incorrect. It means exactly that. Because you can map every number of s3 to every number in s1, it absolutely means they are the same size of infinity.

Again: you said it yourself: if you can map 1-1, then they are the same size. If you can't, if you have numbers left over such as {4}, then they are not the same size. So put up or accept you are wrong: what number in s3 can't be matched to s1?

Grey Wolf

If you match every value in S1 to S3 then you cannot match the additional values of S3 back to S1 as all the infinite items in S1 are already covered by an a limited set of infinite items in S3- I think this is less clear then what I said above and as I said above I don't know how to explain this any clearer then I already have.

I think we might just be at an impasse here - I think (could be wrong) that I am getting what you are saying, I am not sure that you are getting what I am saying (maybe you are) but assuming both of us understand the other - then we disagree.

[Bacon Elemental]

If you match every value in S1 to S3 then you cannot match the additional values of S3 back to S1 as all the infinite items in S1 are already covered by an a limited set of infinite items in S3- I think this is less clear then what I said above and as I said above I don't know how to explain this any clearer then I already have.

I think we might just be at an impasse here - I think (could be wrong) that I am getting what you are saying, I am not sure that you are getting what I am saying (maybe you are) but assuming both of us understand the other - then we disagree.

I'm no infinity expert but I think the Hilbert Hotel conjecture covers this? If you add 1 to infinity you still have infinity, so an infinite number of additional numbers can be added to any infinite set right? You can never "fill up" an infinite set

[brian 333]

The trouble is, it really does not matter if you can logically cancel every possible item in one bounded infinite set then demonstrate that there are items in the other bounded infinite set that remain uncanceled. This only demonstrates that the two bounded infinities have different components.

Let us assume one set has infinite elephants and the other has infinite elephants and gazelles. Cancel all the elephants and one set is empty and the other still has infinite gazelles. Naturally, the set with gazelles is larger. Logical.

But, with infinity, one cannot cancel. The set with only elephants can match an elephant to every elephant and gazelle you could ever line up. The thing about infinities is that no matter how many you cancel, there are more. Since all infinities are infinite, the only cancellation that works is the whole set.

If one is comparing two bounded infinities then divides one of them by two, one is now comparing the first infinity to half-infinity plus half-infinity. This is where logic fails. You can't have half an infinity. Dividing a bounded infinity by any means creates two bounded infinities.

In the All Whole Numbers set vs All Integers set comparison, one attempts to divide the Integers set. Doing so results in two bounded infinities, one of which is used to cancel the Whole Numbers set.

A ÷ A = 1
(A/2 + A/2) ÷ A = 1

So, by cancellation, let us cancel A/2, (a bounded infinity,) by A (another bounded infinity.)

A/2=1

See the problem?

But brian, we are doing A ÷ B!
No. We are dividing infinity. Infinity divided by anything equals infinity every time. The only thing that cancels infinity is infinity.

Bounded infinities never contain more or less units than any other infinity. The bounds only describe what kinds of things we find in that infinity.

[dancrilis]

I'm no infinity expert but I think the Hilbert Hotel conjecture covers this? If you add 1 to infinity you still have infinity, so an infinite number of additional numbers can be added to any infinite set right? You can never "fill up" an infinite set

Effectively yes, that doesn't however mean that there are not greater and lesser infinities.

To the extent that you can map infinities you can map a greater infinity into a lesser infinity (not on same with same) and you can map a lesser infinity into a greater infinity (on basis of same with same, or otherwise) - but you cannot map the totality of a lesser infinity into a greater infinity (mapping on the basis of same with same) and then map the remaining elements of the greater infinity back into the lesser infinity as any element you would choose within the lesser infinity would already be in use.

At least not in the examples I was using.

[Grey_Wolf_c]

If you match every value in S1 to S3 then you cannot match the additional values of S3 back to S1 as all the infinite items in S1 are already covered by an a limited set of infinite items in S3- I think this is less clear then what I said above and as I said above I don't know how to explain this any clearer then I already have.

No. This is false. You are wrong. You clearly can match every single value in S1 to every single value in S3 with none left over in either side. If you think this is not the case, then give me a number that can't be matched.

No more "trying to explain it clearer". No more declarations like the one above that you think are true when they are not. Either produce one counterexample, or accept you are wrong.

This is basic infinite set math concept. You are wrong about this, and the fact you can't find a counterexample proves you are wrong. If you can't accept that you are wrong, then go ahead and start reading about infinite set theory in wikipedia, or even in Irregular Wbcomic (Jasdoif gave you the link), or even look up Hilbert's Infinite hotel on youtube. But save me from another declaration like "If you match every value in S1 to S3 then you cannot match the additional values of S3 back to S1 as all the infinite items in S1 are already covered by an a limited set of infinite items in S3", which is clearly nonsense. I gave you the formula that matches them. Try it yourself. Try it until you find a number that isn't covered by the formula. If I was wrong and you were right, there should be infinite number of them. Either find one, or accept you are completely wrong about this.

Effectively yes, that doesn't however mean that there are not greater and lesser infinities.

Yes there are. The infinite set of Natural numbers is smaller than the infinite set of the Reals. But no subset of any type of number is any bigger or smaller than any other subset of the same type of number, nor is it any smaller than the whole set of that type of number. Interestingly, the infinte set of the Natural numbers is the same size as the infinite set of the Integers, and indeed the same size as the Rationals. But all three sets are smaller type of infinite than the infinite set of the Reals.

Grey Wolf

[dancrilis]

No. This is false. You are wrong. You clearly can match every single value in S1 to every single value in S3 with none left over in either side. If you think this is not the case, then give me a number that can't be matched.

No more "trying to explain it clearer". No more declarations like the one above that you think are true when they are not. Either produce one counterexample, or accept you are wrong.

This is basic infinite set math concept. You are wrong about this, and the fact you can't find a counterexample proves you are wrong. If you can't accept that you are wrong, then go ahead and start reading about infinite set theory in wikipedia, or even in Irregular Wbcomic (Jasdoif gave you the link), or even look up Hilbert's Infinite hotel on youtube. But save me from another declaration like "If you match every value in S1 to S3 then you cannot match the additional values of S3 back to S1 as all the infinite items in S1 are already covered by an a limited set of infinite items in S3", which is clearly nonsense. I gave you the formula that matches them. Try it yourself. Try it until you find a number that isn't covered by the formula. If I was wrong and you were right, there should be infinite number of them. Either find one, or accept you are completely wrong about this.

Grey Wolf

As I mentioned I felt this was going to go this way:

If you hold that I am wrong (which you seem to)...

...

... both of us thinking the other should 'go read a book' (or 'take a course' or some other such related thought pattern) ...

I think your entire approach to this is faulty - I see no reason to make use of a faulty approach (i.e find an example).

I have acknowledged that you can map a larger infinity into a smaller one (I don't believe I ever said you couldn't) - that has never been what I was talking about, merely that larger infinities exist and that 1 to 3 is a larger infinity then 1 to 2 as you can extract any and all numbers between 1 to 2 from 1 to 3 and have items remainding you cannot extract all the numbers within 1 to 3 from 1 to 2 as 1 to 2 does not have all the numbers that 1 to 3 has - you disagree, thats fine.

[Grey_Wolf_c]

I see no reason to make use of a faulty approach (i.e find an example).

You quite literally claim to believe that if you match every number from S1 to S3, there will be S3 numbers left over, and yet "you see no reason" to prove this?

I have acknowledged that you can map a larger infinity into a smaller one (I don't believe I ever said you couldn't) - that has never been what I was talking about, merely that larger infinities exist and that 1 to 3 is a larger infinity then 1 to 2 as you can extract any and all numbers between 1 to 2 from 1 to 3 and have items remainding you cannot extract all the numbers within 1 to 3 from 1 to 2 as 1 to 2 does not have all the numbers that 1 to 3 has - you disagree, thats fine.

No, I don't "disagree". This is not a matter of opinion. It is a mathematical fact that S1 and S3 have the same type of infinites. Every number of S3 can be matched to a unique number of S1. Every number of S1 can be matched to a unique number of S3. I have given you the formula for it. This is not down to a matter of opinion, anymore than if the Earth is flat or a sphere is a matter of opinion.

I was willing to believe that you could be guided to the realisation that you are wrong. But "I see no reason to make use of a faulty approach (i.e find an example)" is a baffling assertion. You are effectively refusing to prove your position, just declaring it right and above any testing.

GW

[linkhyrule5]

As I mentioned I felt this was going to go this way:


I think your entire approach to this is faulty - I see no reason to make use of a faulty approach (i.e find an example).

I have acknowledged that you can map a larger infinity into a smaller one (I don't believe I ever said you couldn't) - that has never been what I was talking about, merely that larger infinities exist and that 1 to 3 is a larger infinity then 1 to 2 as you can extract any and all numbers between 1 to 2 from 1 to 3 and have items remainding you cannot extract all the numbers within 1 to 3 from 1 to 2 as 1 to 2 does not have all the numbers that 1 to 3 has - you disagree, thats fine.

Math is not a matter of opinion. You are simply wrong. "Find an counterexample" is one of two correct ways to prove the negation of a statement, the other being to prove the contrapositive (i.e. show that the contrapositive is equivalent to TRUE/is a tautology); there are no others, you do not get to make up your own axioms (not since Peano anyway.)

Indeed there are larger and smaller infinities, but dividing up the reals does not produce an infinity of a different size. Your problem is that you are trying to match up each number from one set to the same number of the second set, but this is unnecessary. All that is necessary is to come up with any one-to-one (i.e. invertible) mapping. The existence of a mapping that does not cover the second set does not prove the nonexistence of a mapping that does cover the second set. As long as an invertible map exists, then the sets must have the same cardinality.

[Laurentio III]

Well now, my understanding is that the ratio of puns continues to increase, but the number of rape and sexual assault references threatens to overtake them later. So...depends on what you consider "better."

One of the reason I stopped reading the author entirely. The "Incarnations" series was quite good, but in the end turned in a step-by-step guide about mature men and underage girls romance.

[dancrilis]

You quite literally claim to believe that if you match every number from S1 to S3, there will be S3 numbers left over, and yet "you see no reason" to prove this?

Yes - I hold this to be self-evident.

Humans exist.
I have internet access.
You have internet access.
As S3 has S1 within it and also has additional elements beyond S1 if you extract S1 from S3 there will be items remaining in S3.

Proving any of the above could likely be done but attempting to prove such to someone who doubts such seems like an odd task to set for myself.

Now perhaps I am some other animal and humans don't exist and I lack internet access and you don't exist and have no internet access and all of reality is some fever dream I am having - but I see no reason to engage with that thought process.

No, I don't "disagree".

Great.

I was very tempted to simply leave the rest of this post untyped, but such would seem unfair (a perhaps more then a little unpleasant on my part).

Every number of S3 can be matched to a unique number of S1. Every number of S1 can be matched to a unique number of S3.

This is correct for any number that can be given - however if you match every number from S1 to the same number in S3 (or visa versa) then there will still be unmatched numbers in S3.

[Grey_Wolf_c]

This is correct for any number that can be given - however if you match every number from S1 to the same number in S3 then there will still be unmatched numbers in S3.

Prove. It.

GW

[dancrilis]

Prove. It.

GW

I think I have.

Set1 contains every number between 1 and 2.
Set2 contains Set1 and the number 7.

If you match every number from Set1 to the same number in Set2 you will have an unmatched 7.

[Grey_Wolf_c]

I think I have.

Set1 contains every number between 1 and 2.
Set2 contains Set1 and the number 7.

If you match every number from Set1 to the same number in Set2 you will have an unmatched 7.

No. Don't change examples. Prove which number in S3 is not matched 1-1 with a number in S1, using the formula I gave you.

Give me 1 number in S3 that will still be unmatched after S1n = ((S3n-1)/2) +1

S3n: any number in S3
S1n: it's matching number in S1

GW

[Edreyn]

Oh dear... I really wasn't expecting to start such a dispute on mathematics!

As for Piers Anthony, yes the amount of sexual humour in his books, except first few did more harm then good to books quality.

[dancrilis]

No. Don't change examples. Prove which number in S3 is not matched 1-1 with a number in S1, using the formula I gave you. I.e. prove this assertion you just made:
"if you match every number from S1 to the same number in S3 then there will still be unmatched numbers in S3."

Give me 1 number in S3 that will still be unmatched after S1n = (S3n-1)/2 +1

S1n: any number in S1
S3n: it's matching number in S3

GW

I am not trying to match numbers on a mapping I am matching them directly - I have always been matching them directly to highlight that there would a leftover, I have fully granted that if you apply a mapping you can map a 1-3 into 1-2.

Hence why I feel giving you an example that matches your scenario would be faulty - it has never been in debate.

If you wish to review the post again you will see I said: "if you match every number from S1 to the same number in S3 then there will still be unmatched numbers in S3."

Bolded the 'same' for clarity.

[Laurentio III]

We could open a new thread about tangent discussions in OOTS discussion threads.

#1354 : "Bald superheroes, application of gravity wells in daily life and why cats don't bark"
#1355 : "Which Star Trek official would better fit in Star Wars, forks in history and at what age is proper to flee in a different country"
#1356 : "Proof of ghosts, are paper books better than digital, "boobs" is an inherently funny word and why pasta shape is such important?"

[Grey_Wolf_c]

I am not trying to match numbers on a mapping I am mapping them directly - I have always been mapping them directly to highlight that there would a leftover, I have fully granted that if you apply a mapping you can map a 1-3 into 1-2.

But if you use my formula, you see that it can be done. Every number in S1 matches to every number in S3. That such formula exist proves they are the same size. That you can come up with a different formula to match them that doesn't work is irrelevant; it just shows you don't know what you are doing. If the formula exists, then they are the same size. Again, this is basic infinite set theory. If the two sets can be mapped 1-1, then they are the same size. If you disagree with what this formula is telling you, if you really think there are infinite numbers in S3 left unmatched, give me one. Otherwise, I am right, and you are wrong. Not "in my opinion", not "maybe". I am right, you are wrong as a matter of mathematical fact.

You are saying the infinite set equivalent of 1 ≠ 2/2. That you think it is self evident that "one" is a different number from "two halves". And when told that is not the case, that we should agree to disagree.

Hence why I feel giving you an example that matches your scenario would be faulty - it has never been in debate./quote]

If you wish to review the post again you will see I said: "if you match every number from S1 to the same number in S3 then there will still be unmatched numbers in S3."

Bolded the 'same' for clarity.

Don't care what you say. This is what set math says:

Infinite Sets
An infinite set is a non-empty set which cannot be put into a one-to-one correspondence with {1,2,3,...,𝑛} for any 𝑛∈ℕ .

Same Cardinality
If set 𝐴 and set 𝐵 have the same cardinality, then there is a one-to-one correspondence from set 𝐴 to set 𝐵

A bijection (one-to-one correspondence), a function that is both one-to-one and onto, is used to show two sets have the same cardinality.

I have given you the function that proves the bijection. Both S1 and S3 have the same cardinality. If you still think I am wrong, the counterexample is to give me any of the infinite numbers in S3 that are not covered by my formula.

But I am not wrong. You are.

Grey Wolf

[dancrilis]

If you still think I am wrong

Nope changed my mind on that after I figured out what you meant, see here.

I get what you are saying (I believe) and you are not wrong - it is simply nothing to do with what I was saying.

I stand by that statement (potentially grammer aside I suppose).