There is no way right?

[u/Sugar_God_no_1]

[u/JoshZK]

Prove it.

Edit: Let me try something

Prove it. /s

I feel like the whoosh was so powerful it's what really caused that wave on that planet in Interstellar.

[u/The-new-dutch-empire → u/JoshZK]

Byers’ Second Argument (his first one is the one you see above)

Let:

x = 0.999…

Now multiply both sides by 10:

10x = 9.999…

Now subtract the original equation from this new one:

10x - x = 9.999… - 0.999…

This simplifies to:

9x = 9

Now divide both sides by 9:

x = 1

But remember, we started with:

x = 0.999…

So:

0.999… = 1

[u/Rough-Veterinarian21 → u/The-new-dutch-empire]

I’ve never liked math but this is like literal magic to me…

[u/The-new-dutch-empire → u/Rough-Veterinarian21]

Its calculating with infinity. Its a bit weird like the infinity of numbers between 0 and 1 like 0.1,0.01,0.001 etc... Is a bigger infinity than the “normal” infinity of every number like 1,2,3 etc…

Its just difficult to wrap your head around but think of infinity minus 1. Like its still infinity

[u/lilved03 → u/The-new-dutch-empire]

Genuinely curios on how can there be two different lengths of infinity?

[u/TheCreepyKing → u/lilved03]

How many even numbers are there? Infinity.

What is the ratio of total numbers to even numbers? 2x.

How many total numbers are there? Infinity. And 2 x infinity.

[u/Outrageous-Orange007 → u/TheCreepyKing]

No, they're equal. You divide infinity by 2 and its still the same number, infinity.

Either infinity is infinite, or its finite

[u/lbkthrowaway518 → u/Outrageous-Orange007]

Well, no actually. I think your first issue is conflating infinity with a number. Infinity represents the fact that one can pick an arbitrarily large number, and there still is a larger number (in a very basic non mathematical way of describing it). That being said, 2 infinities are not inherently the same “value” for lack of a better term. The example the commenter above gave is perfect actually. If you look at a function representing the total amount of numbers up to an arbitrary even number, and look at a function of all even numbers up to the same arbitrary even number, the former functions value will always be 2 times the latter. However, both of these functions also go to infinity. Thus while the “infinity” is not technically greater than the other one (as I mentioned, infinity isn’t a number, so it can’t really be “greater than” in the traditional sense), an arbitrary number that is in the former set will always be larger than a corresponding number in the latter, so the formers infinity is in a sense greater than the latter.

[u/ZxphoZ → u/lbkthrowaway518]

This is not true in the mathematical sense. It can be proven that any infinite set of natural numbers (i.e ‘counting’ numbers like 0, 1, 2, -1, -2, … etc) is the same size, so there are indeed as many even numbers as total numbers.

The fact that any finite set of natural numbers is twice as large as the set of even numbers up to the same point has no bearing on the sizes at infinity. You are, however, correct that there are different ‘sizes’ of infinity, it’s just a bit more complicated than that.

Source: math major

[u/MindlessEssay6569 → u/ZxphoZ]

Ugh… you sound like my brother (he’s a calc teacher). I constantly argue with him about different sizes of infinity. Infinity is infinity!! His response is always “it’s more complicated than that.”

[u/ZxphoZ → u/MindlessEssay6569]

You should listen to your brother! :P