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It's a series of misspellings, puns, and tortured logic. > It has two hind legs, aside from its fourlegs. Hind legs are the opposite of forelegs so the statem

It's a series of misspellings, puns, and tortured logic. > It has two hind legs, aside from its fourlegs. Hind legs are the opposite of forelegs so the statement is true but misspelled, and [---tortured logic here---] two hind legs plus "four" forelegs totals to six legs. > Which means it has six legs... Now six is an even number, so it must have an even number of legs... But six is an odd number of legs for a horse to have, so it has an odd number of legs. Six is an even number but it's "odd" - as in strange - for a horse to have six legs so horses [---tortured logic here---] must also have an odd - as in mathematical - number of legs. > The only number that is both odd an even is infinity. Since a horse has both an odd an even number of legs, it must have infinite legs. Infinity is a complicated "number" with different interpretations and [---tortured pure math here---] if you stretch some of them to the breaking point, the only horse that can have both an "even" and an "odd" number of legs is one that "must have infinite legs" > But there is one horse, that not only has an infinite number of legs, it has legs that are infinitely long. This plays on the ambiguity of "infinite legs" which could mean an "infinite number of legs" or "infinitely long legs". All in all, thumbs up. Cost me some cherry switches thanks to projectile tea.

thaumasiotes 4y ago
> Infinity is a complicated "number" with different interpretations and [---tortured pure math here---] if you stretch some of them to the breaking point, the only horse that can have both an "even" and an "odd" number of legs is one that "must have infinite legs" I am not aware of this math; can you elaborate? In pretty much any system, there is no number that is both even and odd, and including infinite quantities in the system doesn't change that.
- naet 4y ago
  Infinity is an infinitely high number. What is Infinity plus one? It must still be Infinity, since it's already infinitely high and can't go any higher. But if you have an odd number and add one, you get an even number (and vice versa). For Infinity = Infinity + 1 to hold true, Infinity must be both odd and even. Or something like that. It's probably more accurate to say Infinity is neither odd nor even. If you add 2+2+2+2... up to infinity, it might appear even. But that could also be equivalent to 1+3+1+3+1... to infinity, which would be alternating even and odd. Or 1+2+2+2+2... which would always be odd. Infinite quantities bend or break a lot of typical rules that other rational numbers follow.
  - Swizec 4y ago
    If I remember my college set theory correctly, this is because there are infinite infinities. 2+2+2+… is a different infinity than 2+1+2+1+… You can construct infinite sets of numbers that do not overlap. Odd vs. Even infinity is the example our professor used in class to show the concept. I don’t remember enough to replicate here.
    - greggertt 4y ago
      Wow way to kill the enjoyment of a nonsense verse
      - Swizec 4y ago
        Nah the verse was wonderful, I thoroughly enjoyed it.
    - thaumasiotes 4y ago
      In the ordinal-numbers model that your notation leans toward, 2+2+2+... and 2+1+2+1+... are definitely the same infinity, both ω. On the other hand, you reminded me that conditionally convergent series may converge to different sums depending on how you choose to group their terms, which is fun. (That is, [(s_1 + s_2) + s_3 + (s_4 + s_5) + s_6 + ...] may have a different sum than [(s_1 + s_2) + (s_3 + s_4) + (s_5 + s_6) + ...] does.)† † I hope this is true; I can't find a cite for it. The more famous theorem is that you can get any sum you want by reordering the terms, but I think regrouping is good enough to get you different sums, if not arbitrary sums. ----- Thinking about it more, the idea would be that the sum of a series is of course the limit of the sequence of partial sums. By artfully parenthesizing the terms of an original series, we can reduce it to a new series with a different sequence of partial sums. This sequence must be a subsequence of the original sequence -- parenthesizing the series essentially just means ignoring certain partial sums. So then the question, if we're willing to start waving our hands, is "when (infinite) sequence S has limit L, and (infinite) sequence S' is a subsequence of S, must S' also have limit L?". The infinitude of S' is going to require the answer to be yes, so regrouping will end up not being good enough to change the sum of a conditionally convergent series. Sorry. :( However, if a series does not converge or diverge, such that its sequence of partial sums has multiple limit points, artfully parenthesizing the terms of that series should be able to get you a new series that converges on any limit point of the old one.
- lozenge 4y ago
  A set is even if you can pair each element up with another element. A set is odd if you can pair each element with another element and have one element left over unpaired. Then infinity is even and odd.

thaumasiotes 4y ago

> Infinity is a complicated "number" with different interpretations and [---tortured pure math here---] if you stretch some of them to the breaking point, the only horse that can have both an "even" and an "odd" number of legs is one that "must have infinite legs" I am not aware of this math; can you elaborate? In pretty much any system, there is no number that is both even and odd, and including infinite quantities in the system doesn't change that.

naet 4y ago
Infinity is an infinitely high number. What is Infinity plus one? It must still be Infinity, since it's already infinitely high and can't go any higher. But if you have an odd number and add one, you get an even number (and vice versa). For Infinity = Infinity + 1 to hold true, Infinity must be both odd and even. Or something like that. It's probably more accurate to say Infinity is neither odd nor even. If you add 2+2+2+2... up to infinity, it might appear even. But that could also be equivalent to 1+3+1+3+1... to infinity, which would be alternating even and odd. Or 1+2+2+2+2... which would always be odd. Infinite quantities bend or break a lot of typical rules that other rational numbers follow.
- Swizec 4y ago
  If I remember my college set theory correctly, this is because there are infinite infinities. 2+2+2+… is a different infinity than 2+1+2+1+… You can construct infinite sets of numbers that do not overlap. Odd vs. Even infinity is the example our professor used in class to show the concept. I don’t remember enough to replicate here.
  - greggertt 4y ago
    Wow way to kill the enjoyment of a nonsense verse
    - Swizec 4y ago
      Nah the verse was wonderful, I thoroughly enjoyed it.
  - thaumasiotes 4y ago
    In the ordinal-numbers model that your notation leans toward, 2+2+2+... and 2+1+2+1+... are definitely the same infinity, both ω. On the other hand, you reminded me that conditionally convergent series may converge to different sums depending on how you choose to group their terms, which is fun. (That is, [(s_1 + s_2) + s_3 + (s_4 + s_5) + s_6 + ...] may have a different sum than [(s_1 + s_2) + (s_3 + s_4) + (s_5 + s_6) + ...] does.)† † I hope this is true; I can't find a cite for it. The more famous theorem is that you can get any sum you want by reordering the terms, but I think regrouping is good enough to get you different sums, if not arbitrary sums. ----- Thinking about it more, the idea would be that the sum of a series is of course the limit of the sequence of partial sums. By artfully parenthesizing the terms of an original series, we can reduce it to a new series with a different sequence of partial sums. This sequence must be a subsequence of the original sequence -- parenthesizing the series essentially just means ignoring certain partial sums. So then the question, if we're willing to start waving our hands, is "when (infinite) sequence S has limit L, and (infinite) sequence S' is a subsequence of S, must S' also have limit L?". The infinitude of S' is going to require the answer to be yes, so regrouping will end up not being good enough to change the sum of a conditionally convergent series. Sorry. :( However, if a series does not converge or diverge, such that its sequence of partial sums has multiple limit points, artfully parenthesizing the terms of that series should be able to get you a new series that converges on any limit point of the old one.
lozenge 4y ago
A set is even if you can pair each element up with another element. A set is odd if you can pair each element with another element and have one element left over unpaired. Then infinity is even and odd.