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.

MPrimeFinder · 2022-09-25, 13:08

Quote:

Originally Posted by VBCurtis

Sure! They look like exactly the same size of infinity to me.

Infinity is just a variable, so 2∞ and even ∞∞ (∞²) exist.

xilman · 2022-09-25, 16:47

Quote:

Originally Posted by paulunderwood

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

And do you believe in the CH?

lavalamp · 2022-09-25, 17:30

Quote:

Originally Posted by xilman

And do you believe in the CH?

Yes, it is the 4th letter of the Welsh alphabet, and appears twice in church, although I don't go there myself.

PhilF · 2022-09-25, 17:36

Yes, I believe in hydrocarbons, although you're going to have to include some O's with your CH's.

paulunderwood · 2022-09-25, 18:42

Quote:

Originally Posted by xilman

And do you believe in the CH?

Wasn't that conundrum settled by Paul Cohen. It had something to do with the ZFC axioms. The whole notion drove Cantor to the sanatorium.

2022-05-18, 13:36	#23
retina Undefined "The unspeakable one" Jun 2006 My evil lair 6,689 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 6,689 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.

2022-09-25, 17:36	#32
PhilF "6800 descendent" Feb 2005 Colorado 2·3²·41 Posts	Yes, I believe in hydrocarbons, although you're going to have to include some O's with your CH's.