Infinite question

So… I just got done watching a video on the term “Infinity.” I would like to talk about it.

First of all, most people would like to think Infinity is 1-2-3-4-5-6-7-8-9-and so on. Even though that is true, infinite is truly a lot more than that.

Let’s take integers for example. There is 1, 2, 3, 4, 5, and there’s also 1, 0, -1, -2, and so on.

Then there’s decimals. You can any whole number by adding a decimal point (.) to the end of it and putting any digits (Besides 0 of course). So let’s take the number 1, for example. There is, of course, 1. But than 1.1, 1.11, 1.111, 1.1111, than 1.2, 1.22, 1.222, and so on.

So, couldn’t we say that between any 2 whole numbers, there are an infinite number of decimals?

Then there’s fractions. 1/2, 1/3, 1/4, 1/5. There’s also 2/100, 9/1098, even 1.9/99.35. Then there’s top heavy fractions, 4/2, 5/2, 6/2, and 9.9/10

So it’s not just 1, 2, 3, 4, 5.

But …1, ∞, 2, ∞, 3, ∞, 4, ∞, 5, and so on.

lol. Not sure if troll or 13 year old calculus enthusiast o-o

just because there are an infinite amount of fractions in between each integer you can’t place it as a value on the number line.

ZZZZZzzzzzzz

yes, you could postulate an adoption of ∞² as a number seperate from ∞.

Originally posted by Frank101:

So, couldn’t we say that between any 2 whole numbers, there are an infinite number of decimals?

Nope.

decimal numbers. there are an infinite amount of decimal numbers between each two integer numbers.
and theoretically, between each decimal number and the next, although there can be no next because there’s an infinite amount, but still between each two consequent decimal numbers there are in theory an infinite amount of irrational numbers.

Originally posted by TheKnifeGrinder:

i am not a mathematician lol but i think that infinity is a series of numbers that never ends.. if we talk about numbers..

0,1
0,11
0,111
etc etc forever

or in a binary system

0
01
010
0101
etc etc forever

√2 is the example where u have infinite decimals but in real world it has a definite numbers of decimals that made it.. it s like saying if at some point after the particles the matter finish or keep existing.. nobody knows yet..

tl;dr

Infinity is a concept, not a number.

The fun thing about real numbers is this:

Pick any two distinct numbers. There are infinitely many real numbers between the two you have chosen. Additionally, the interval you created has just as many numbers as there are real numbers without restriction.

Yeah. Real analysis is a dick like that.

(I’m phrasing this all rather loosely, in an effort to avoid technical details.)

This same concept is used for an argument (The name I can’t recall) that tries to prove that we can never be more than half way to our destination, by means of an infinite number of ‘halves and halves of halves and halves of those’ making reaching any one point impossible due to the infinite number of halves that must be crossed.

^ Xeno’s paradoxes.

Also I don’t know much about it, but in mathematics there are actually infinities of different sizes. The number of real numbers, for instance, is greater than the number of integers, despite the fact that they are both infinite in the general sense of the word.

More specifically, Achilles and the tortoise. I vaguely recall a short story that made fun from this, but I can’t seem to find it.

Also, the sum of an infinite number of halves is 1. (That is, 1/2 + 1/4 + 1/8 + … = 1).

And yes, you can construct an infinite number of infinities, although only two are frequently used as I’m aware. The first is the “countable” infinity, also known as Aleph-naught, which is the size of the natural numbers (all positive integers). The second is the “uncountable” infinity, which is the size of the real numbers. You construct higher infinities by taking the size of the power set.

(That is, take the real numbers to be a set. Now figure out every single way you can pull some numbers from it. There are more ways to do this than there are elements, so the size of this new set must be larger.)

infinite is actually just a description.(a sentence)

Originally posted by adv0catus:

tl;dr

Infinity is a concept, not a number.

Basically this.

That’s why metaphysics is a branch of philosophy, not math.

Originally posted by Galdos:

also, how can you answer a question if you don’t read it. get all the info and THEN comment.

Yeah….THAT is a great suggestion.
Try it some time…eh?
Btw…I think this tread is all about # 2.

Congrats; you stumbled upon the density of the real numbers. It’s an interesting concept.

MY BRAIN FUCKING HURTS NOW! _ i should just stick to political disscussions

Does this matter?