It isn't clear to me infinity is a number in the first place. Reification and category mistakes are as much a danger in math as anywhere.
There is a definition for an infinite ordinal, omega.
Is infinity an odd or even number? (2011)
201–210 of 398 posts
Re: Is infinity an odd or even number? (2011)
#202The way I would explain it to a 6 year old would be like this:
Infinity isn't a number really, it's a concept, like the word many or the word few. If someone says they have many of something, you don't think is that odd or even you just know they have a lot of it. Infinity is kind of like that, it explains the idea of things going on forever, not an exact quantity of things like the number 10 or 11.
Re: Is infinity an odd or even number? (2011)
#203Earlier quoted context omitted.
Sqrt(2)/2 can not be written as a decimal number. A decimal number is a rational whose denominator is an integer power of 10.
No, any rational number with a denominator that has only the prime factors of 2 and 5 will have a finite and exact decimal representation in base 10.
That's exactly the same thing as I said, using different words.
And anyway, is Sqrt(2)/2 such a number?
Re: Is infinity an odd or even number? (2011)
#204I’ve always thought infinity is not a number but a concept that represents something which is ever increasing.
It is that as well.
Re: Is infinity an odd or even number? (2011)
#205I want to know if there are more decimal numbers between 0 and 1 than there are integers between 0 and infinity.
There are more reals between 0 and 1 than integers.
There are not more numbers with terminating decimals between 0 and 1 than integers.
Re: Is infinity an odd or even number? (2011)
#206Earlier 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
3.14...
Re: Is infinity an odd or even number? (2011)
#207Earlier quoted context omitted.
It’s also equal to the product of all primes except 2 so it’s odd.
This just implies that infinity is both even and odd, which means that the statement "infinity is even" is still technically correct by this reasoning.
Next you'll tell me light is both particles and a wave. This scientific saucery must stop! Order it to pick one or jailit!
Re: Is infinity an odd or even number? (2011)
#208Re: Is infinity an odd or even number? (2011)
#209 npm i is-even
const isEven = require("is-even");
console.log(isEven(Infinity));
TypeError: is-odd expects a number.Re: Is infinity an odd or even number? (2011)
#210The problem with transfinite is that you lose commutatively. Flowing the standard notation, where the usual infinite in the integer or the real line is "ω = ∞ = 1,2,3,..." ω+1 = ω+1 , i.e. "the next thing after infinity" 1+ω = ω , i.e. "the same infinity as before" 2ω = ω , i.e. "the same infinity as before", so it's even 1+2ω = ω , i.e. "the same infinity as before", so it looks odd, but don't fall in that trap ω2 =…
> After lunch, I went to teach limits to first years students, and with a total straight face I told them that ∞ is not a number.
When you apply Alexandroff extension to add the point at infinity to, say, the real numbers, what you're left with is not a set of numbers (i.e. a field) anymore. So it makes sense to say that ∞ is not a number. Moreover, the way ∞ is used in analysis is different from Alexandroff compactification, in that you usually use two infinities (±∞) as a shorthand for quantification over increasing or decreasing sequences of real numbers (this can be formalized using extended real numbers [0] or other gadgets but doing so has no advantages in a first-year analysis class, and might in fact make matters worse).