Endless Horse
endless.horse
endless.horse
It has two hind legs, aside from its fourlegs.
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.
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.
But there is one horse, that not only has an infinite number of legs, it has legs that are infinitely long.
And here it is!
That doesn’t seem correct: https://math.stackexchange.com/a/49046/429295
"Infinity" without further specification seems more likely to refer to the concept in the extended reals (where there are exactly two infinite numbers) than to refer to the concept of infinite ordinal numbers. The obvious analysis would appear to be that, not being an integer, it cannot be considered either even or odd, but there might be a convention I don't know about.
Simple, that's the only sense of "infinity" that most people know.
But no mare, meaning there is not any mare such that it has five (5) legs.
Thus the cardinality of "no mare" > the cardinality of "mare".
> 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.
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.
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.
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.
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.
This is a mistake. That is how the extended reals behave. There are other systems. The diagonalization argument will already tell you that if you're at infinity, you can still go higher. This is also true for ordinal numbers and nonstandard analysis. It is the general case; the behavior in the extended reals is a special case.
> 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.
This is much worse; your conclusion is unrelated to your premise. You would need an additional premise, that infinity is either even or odd, which you didn't bother to supply. The same argument will tell you that either (a) 1.3 is even and 2.3 is odd, or (b) 1.3 is odd and 2.3 is even. (a) and (b) are both false.
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.
A bet, which has most legs, a mare, or no mare.
A mare, to be sure, replied Ned, with a grin,
And fifty I’ll lay, for I’m certain to win.
Quoth Bob, you have lost, sure as you are alive,
A mare has but four legs, and no mare has five.
- from A Panorama of Wit, 1809, p. 53
You had me until this one. Even the tortured logic made sense to me until this point and it feels like this was just shoehorned in to make it work..unless I'm missing something?
a truthy value is a value that is considered true when encountered in a Boolean context.
It felt good to scroll down again
On the Internet you can remember your name
'Cause there ain't no one horse to give you no pain
Alexander was a great general. Great generals are forewarned. Forewarned is fore armed. But four is an odd number for a general to have. ...
Couldn't the horse have zero legs too?
It's wonderful seeing this pop up occasionally. As boing boing once said, it's not called endless for nothing.
We personally use https://secure.endless.horse/ as a quick check our internet connections, especially when there's a captive portal.
We tried adding endless.horse to a database of non-phishing urls (after all, it's merely an ASCII art horse with abnormally long legs), but the one we were pointed to by the security researchers hasn't allowed new accounts for the last two years. It's a strange being implicated in this indirect way -- Does endless.horse condone phishing? The horse says "neigh."
Endless Horse - https://news.ycombinator.com/item?id=9558687 - May 2015 (15 comments)
The only way to find out is to scroll infinitely as the domain name suggests. Beware, your scrolling may have been finite.
traceroute bad.horse
ofcourse.horse
There used to be walmart.horse.
I'm very vested in this TLD. I originally launched FakeYou.com on jungle.horse, and I have a few more in my back pocket saved up for future occasions.
traceroute bad.horse"The purpose of the .horse gTLD is to offer horse owners, service providers, horse industry employees, and volunteers the opportunity to clearly define their presence on the Internet and to help potential customers gain access to content about horses.
...
We specifically examined more restrictive registration policies, such as limiting registration to members of organizations with a specific tie to horses. We rejected such limitations because they would interfere with .horse’s primary mission, purpose, and goals--which is to encourage as many registrants as possible to associate themselves with horses for any legal purpose."
Who did this?
"MMX, also known as Minds + Machines, applied for the gTLD on behalf of the company and its subsidiary.
...
Minds + Machines Group Limited (MMX) (formerly Top Level Domain Holdings Ltd. (TLDH)) is the parent company of Minds + Machines. The company is dedicated to acquiring and operating new gTLDs, as well as providing consultancy services and back-end registry solutions for entities interested in operating new gTLDs. The company is publicly traded on the AIM under the ticker symbol TLDH.L. Its market cap is valued at over $60 million USD."
Also:
"The application for the .horse TLD is supported by the Lexington Fayette Urban County Government, Keeneland Pony Club, Lexington Convention and Visitors Bureau, The Greater Lexington Chamber of Commerce, Inc., Kentucky Equine Humane Center, and the Inforatag Racing Stable LLC."
edit: woof! at ~80 EUR/year, the joke is maybe not worth it
2 - refresh page
3 - close dev console
the end :)