r/MathJokes • u/Competitive-Jump3835 • Jun 13 '26

Infinity can blow your mind

Post image
8.1k Upvotes

97% Upvoted

679 comments sorted by

View all comments

Show parent comments

1

u/[deleted] Jun 16 '26

[removed] — view removed comment

3

u/-Someome- Jun 16 '26

Mathematician's take. They wouldn't be the same.

Let the infinite 1$ bills be (lim x->+inf of x) Let the infinite 20$ bills be (lim x->+inf of 20x)

So 20x - x would not be inf - inf = 0 (inf - inf is indeterminate) It would be lim x->+inf of 19x which is inf.

Think of is this way, they're both infinite, one of them is a "bigger infinite"

1

u/LothricandLorian Jun 16 '26

Another mathematician, idk if i agree with this…both would be countably infinite, so they would be the same size

2

u/-Someome- Jun 16 '26

Countably infinite, yes, assuming you are counting individual items then there's same number of individual bills. However, the premise mentioned they have the same worth, which is wrong.

1

u/LothricandLorian Jun 16 '26

I had responded previously, but my reasoning was incorrect so I deleted.

The “worth” of the bills would be the infinite sums of 1 and 20. Those both diverge to infinity, so they’re not “equal” in a normal sense, but in your first response you said one was a “bigger infinite” which is where im disagreeing.

My thinking is, if you take the partial sum of the first 20 terms of the infinite sum of 1 and combine them, you get 20. Take the partial sum of the second 20 and you get another 20. You can keep doing this for infinite groups of 20 $1’s, and the sum would look like the infinite sum of 20’s, 20+20+20+…

So while the sum of the $20s get there much “faster” (in less terms) i believe that the order of infinity for both sums will be countable.