/sci/ - Science & Math

[Anonymous No.9509303]

Question:

How do you figure out if there is an infinite amount of something?
Do you count each thing that makes up something?
How long does it take to count to infinity?
How big is infinity × 2?

Only PROFESSIONAL mathemeticians and serious replies are welcome.

[Anonymous No.9509446]

(1)when it is not finite
(2)by assigning numbers to them
(3)an infinite amount of time
(4)infinity

thank you I'll expect my fields medal in the mail any time guys

[Anonymous No.9509455]

There can only be a finite number of objects in the real universe since there are only a finite number of atoms to build them out of.
That limitation doesn't apply in mathematics, which deals with idealizations. There are an infinite number of points on any continuous line-segment and an infinite number of points on any continuous rectangle. The "same" infinity, since the points (though uncountable) can be matched in a one-to-one correspondence. But not all infinities are the same. There are more irrational numbers on a given length of the number-line than there are rational numbers in that same length. Both are infinite, but one is "a higher order of infinity".
It takes forever to count to infinity and 2 x infinity (of a given order) is still infinity (of that same order). If serious;

See https://en.wikipedia.org/wiki/Georg_Cantor
and https://en.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_Grand_Hotel

[Anonymous No.9509466]

>>9509446
This, but I will give a go as well
1) rule out the possibility of a finite amount
2) see 1)
3) infinite amount of time assuming what you're counting is countably infinite, if its uncountably infinite, you could not count it
4) infinitely big

For additional fun look up Riemanns paradox which shows that infinity minus infinity equals any number you want it to

[Anonymous No.9509490]

well the easiest way to "understand" infinity is with natural numbers, you know 1,2,3,... and such, where a adding 1 to the last number will result in another natural number, we can keep doing this forever and we will still get natural numbers, this is a type of infinity.


After this we can "compare" infinities with something that's called cardinality, this way if we are able to form a bijection from one set to another we get that they have the same cardinality, from this we see that the natural numbers have the same "type" of infinity that the integers and the rationals, since we can form a bijection, we can number this type of infinity, so we call this a countable infinity, but then we have things like the real numbers, which are a "bigger" type of infinity, since we can't form a bijection between them and the naturals this means we can't count them, so we call this an uncountable infinity.


If you really care about this start to read set theory, Enderton elements is a good book if you already know how proofs work, after that read Jech's set theory and you will get a good understanding of all this.

[Anonymous No.9509550]

These are all retarded answers.

Say you're in 2nd grade again cause that is obviously where you belong. There is a glass jug of candy at the front of the classroom and every student gets to guesstimate how many pieces of candy are in the jug. Whoever's estimate is the closest to the actual amount gets that student a piece of candy.

How is the actual amount of candy pieces in the jug discovered in order to compare it to the estimates? By counting. The teacher counts the pieces of candy one by one, and thus can make the amount of candy knowable.

You cannot count an infinite amount. You cannot count to infinity, therefore you cannot know an infinite amount even arbitrarily through pure maths. You know what infinity means? It means "i'm not faithfully iterating numbers in thoughtful yields". You are makin up bullshit by using infinity as a number, and saying there is an infinite amount is vague unintelligible nonsense no different than saying "a lot".