Is (1 + 1 + 1 + 1 + 1 + 1 + ...) less than (1 + 2 + 3 + 4 + 5 + 6 + ...) ? - Page 3

retina · 2022-05-18, 13:36

Nice vid.

https://www.youtube.com/watch?v=YuIIjLr6vUA

Supersums, Zeta and Eta functions, are also included for some extra spice.

paulunderwood · 2022-05-20, 02:14

Quote:

Originally Posted by retina

Good job.

Now we have two answers.

A > B, and
B > A

Anyone want to speculate now that A = B?

https://en.wikipedia.org/wiki/Schr%C...nstein_theorem

retina · 2022-05-20, 02:40

Quote:

Originally Posted by paulunderwood

https://en.wikipedia.org/wiki/Schr%C...nstein_theorem

Good job.

Although that says that |A| = |B|. Which is what VBCurtis suggested up thread.

retina · 2022-05-20, 14:42

The infinite product of 2×2×2×2×2×2×2... = 0

If we set p = 2×2×2×2×2×2×2... we can see that 2×2×2×2×2×2×2... = 2×p

Leading to p = 2×p

Subtract p from both side; 0 = p

Giving 2×2×2×2×2×2×2... = 0

Sadly the Mersenne number 2^∞-1 = -1, and therefore isn't prime.

paulunderwood · 2022-05-20, 16:15

Quote:

Originally Posted by retina

The infinite product of 2×2×2×2×2×2×2... = 0

If we set p = 2×2×2×2×2×2×2... we can see that 2×2×2×2×2×2×2... = 2×p

Leading to p = 2×p

Subtract p from both side; 0 = p

Giving 2×2×2×2×2×2×2... = 0

Sadly the Mersenne number 2^∞-1 = -1, and therefore isn't prime.

\[2^{\aleph_0} - 1 = \aleph_1\] and I am not sure primeness is defined for these.

retina · 2022-05-21, 01:26

Quote:

Originally Posted by paulunderwood

2^{aleph_0} - 1 = aleph_1 ...

I showed my working to arrive at the real answer of 0.

2022-05-18, 13:36	#23
retina Undefined "The unspeakable one" Jun 2006 My evil lair 73×89 Posts	The truth about 1+2+3+...=-1_12 Nice vid. https://www.youtube.com/watch?v=YuIIjLr6vUA Supersums, Zeta and Eta functions, are also included for some extra spice.

2022-05-20, 14:42	#26
retina Undefined "The unspeakable one" Jun 2006 My evil lair 73·89 Posts	2^∞ = 0 The infinite product of 2×2×2×2×2×2×2... = 0 If we set p = 2×2×2×2×2×2×2... we can see that 2×2×2×2×2×2×2... = 2×p Leading to p = 2×p Subtract p from both side; 0 = p Giving 2×2×2×2×2×2×2... = 0 Sadly the Mersenne number 2^∞-1 = -1, and therefore isn't prime.