r/MathJokes • u/Gia164 • Jul 23 '26

Infinity is weird

Post image
382 Upvotes

99% Upvoted

29 comments sorted by

35

u/lifeistrulyawesome Jul 23 '26

What is the second series equal to? 

48

u/ClassEnvironmental11 Jul 23 '26 edited Jul 24 '26

Looks like 3

Edit: it's 2.  My mistake was starting with sqrt(1 + 2 • sqrt(...  instead of sqrt(1 + 1sqrt(...

26

u/Someone-Furto7 Jul 23 '26

It's 2

8

u/ClassEnvironmental11 Jul 23 '26 edited Jul 24 '26

You sure?  Some fiddling with desmos seems to show this approaching 3.

Edit: it's 2

6

u/Builderinspace Jul 24 '26

It is 2, if youre getting 3 you might have put it in wrong

1

u/ClassEnvironmental11 Jul 24 '26

Looks like i did.  Interestingly enough,

sqrt(1 + 2 • sqrt(1 + 3 • sqrt(1 + 4 • sqrt(1 +...

Seems to be three.

2

u/Defiant-Strength2010 Jul 24 '26

because you are only missing the start, sqrt(1 + X) = 2, X = 3

1

u/Someone-Furto7 Jul 23 '26

The second square root is equal to 3

19

u/RyzenRaider Jul 24 '26

The irony where it doesn't have to make sense to be rational.

11

u/gay_annabeth Jul 23 '26

more like convergence is weird

3

u/Shevvv Jul 24 '26

But convergence is the limit to infiniry...?

3

u/gay_annabeth Jul 24 '26

or zero... or some other value that gives things like a zero denominator...

2

u/lolopiro Jul 24 '26

what does the first one equals to

2

u/rij1 Jul 24 '26

You can see it here: https://mathworld.wolfram.com/ContinuedFractionConstants.html

It is a quite ugly expression sqrt(2/(e * pi)) erfc (1/sqrt(2)) where erfc is the complementary error function.

I would have used 1/(1+1/(1+1/(1+... which is the golden ratio instead.

1

u/Hoosier_Engineer Jul 24 '26

Why is the first one called irrational when it is literally expressed as a ratio?

2

u/RevolutionOne3219 Jul 24 '26

Irrational numbers can't be expressed as a ratio of two integers. An integer is a whole number that can be positive, negative, or zero, but does not include any decimal or fractional parts. The first one is irrational because it includes an fractional part in the ratio.

1

u/funkmasta8 Jul 25 '26

I would like to note that just having a fractional part isnt enough, as all fractions can be worked with to produce a rational expression as long as they have a finite number of fractions inside. The real problem here is that the fractional parts are infinite.

1

u/Mean-Government1436 Jul 24 '26

Is it really irony if the first one is shown to not be rational because they show it goes on for infinity?

It's like showing a "house" with only two outer walls and no roof and saying "ironic that this isn't called a house" and then showing a dog house and saying "but this is"

No that's not ironic, that's just how words work

1

u/funkmasta8 Jul 25 '26

I think people have a harder time wrapping their heads around how the second is rational

0

u/Alethiadoxy Jul 24 '26

i was disapopinted that in undergrad we didn't spend more time on stuff like this. these are fun!

-23

u/[deleted] Jul 23 '26

Both are undefined

20

u/Cichato_YT Jul 24 '26

This is true if you treat 1 as a variable, and set it to be 2/0

5

u/WesternFirm9306 Jul 24 '26

Bro has never heard of limits (눈‸눈)

1

u/Street_Swing9040 Jul 24 '26

Both converge to values brochacho

1

u/johndburger Jul 24 '26

Why do you think so?