131–140 of 398 posts
I really hate these mathematical technicalities spawned from material implication, chosen way of making a definition and vacuous truth - why can't we even consider some questions to be marked as non-sense/non-relevant like in relevance logic?
>To explain the idea to a child, I would focus on the principal idea: whether finite or infinite, a number is even when it can be divided into pairs. For finite sets, this is the same as the ability to divide the set into two sets of equal size, since one may consider the first element of each pair and the second element of each pair. The answer this quote came from is amazingly obtuse, but it does make me think that…
Infinities aren’t comparable for equality… are they?
I really hate these mathematical technicalities spawned from material implication, chosen way of making a definition and vacuous truth - why can't we even consider some questions to be marked as non-sense/non-relevant like in relevance logic?
There are an infinite number of questions, answers, and topics that were considered nonsense, not written about, and impossible to post to HN.
>To explain the idea to a child, I would focus on the principal idea: whether finite or infinite, a number is even when it can be divided into pairs. For finite sets, this is the same as the ability to divide the set into two sets of equal size, since one may consider the first element of each pair and the second element of each pair. The answer this quote came from is amazingly obtuse, but it does make me think that…
> it does make me think that infinity must be even since infinity can be divided into 2 pairs, each of which is of equal size since both are infinity. This is true, but the same is true of (infinity - 1) Therefor infinity must also be odd.
If you are thinking about the difference between
[0,1,2,3,…]
0, [1,2,3,4,…]
Earlier quoted context omitted.
Yes, but you'll see "decimal" more in the wild, and that's what people mean by it. "You write it with a decimal point", and they do usually mean to include the irrationals. So, yes, real numbers, but the reasoning behind their usage is "you write it with a decimal point". I'd bet more people understand "decimal number" used in that sense, than understand "real number".
i've never seen an irrational number written in digits in my whole life. Have you????? I've seen them expressed as letters or formule
Earlier quoted context omitted.
I don't usually use that term, but I take it to mean "number you (may, and, if not using e.g. fractions, must) write using a decimal point" because that seems to always be what people intend by it. Everybody experienced writing irrational numbers using decimal notation in school, so those definitely count.
> Everybody experienced writing irrational numbers using decimal notation in school, To be pedantic, we experienced writing approximations of these numbers in decimal arithmetic.
So there seems like a glaring hole in the answer, but maybe I'm missing something. Because: > It is easy to prove from this definition by transfinite recursion that the ordinals come in an alternating even/odd pattern, and that every limit ordinal (and hence every infinite cardinal) is even. Sure, if we use the natural numbers and start at 1, then we can group: [1, 2], [3, 4], [5, 6], ... and prove infinity is even.…
So there seems like a glaring hole in the answer, but maybe I'm missing something. Because: > It is easy to prove from this definition by transfinite recursion that the ordinals come in an alternating even/odd pattern, and that every limit ordinal (and hence every infinite cardinal) is even. Sure, if we use the natural numbers and start at 1, then we can group: [1, 2], [3, 4], [5, 6], ... and prove infinity is even.…
I would weaken the definition of even/odd to say that a set is even if /there exists/ a way to pair things off, and odd if /there is no way/ to pair things off (ie, not even). So the countable numbers would be even.