There is a fine line between Genius and Madness.

According to Quantum Religion, this fine line is not Infinitely Small, but has a limit called Planck Length.

]]>Actually they get infinately small…

Cantor is famous also because of the massive backslash of his theory. Infinites have driven people into religion and madness (whatever the difference between the two).

It is not productive to speculate about infinites just as it is not productive to speculate on quantum theory.

]]>The size of infinities is infinite

Actually they get infinately small…

Ask yourself a question,

“How far appart are two points in a space?”

We know that an ordinary measure can be done by taking an arbitary integer N and scalling it to fit.

We also know that between each integer of N is an infinate number of reals. So N x Infinities, with the distance between them being 1/(N x Infinities). So far so easy you would think…

But what lies between each real? And what is there spacing?

So what is the actual space between the reals?

But more importantly how do you tell one real from another real?

Time to find good room service 😉

]]>“What is the difference as far as printing is concerned, of an integer of infinite length and a real of infinite length?”

Well, if it is an Integer, then it can not be infinite, because, by definition, it is fixed. It is not an irrational number that has infinite digits.

Cantor was not in the printing business.

He missed his calling.

Fine print in the license: You are only allowed to print irrational numbers on this printer.

Clippy; It looks like your paper and ink are getting low. Confirm reorder?

]]>If you can prove Cantor wrong, prepare yourself for the Fields medal.

I would have no wish to be “so blessed” or for that matter inflict such “a blessing” on others. Living in a floodlit goldfish bowl is not something anyone should have to suffer.

But my intent was to point out that there is a very real difference between the theory of numbers and the practical reality of expressing numbers in a tangible form no matter how long.

The point being that a programme deals with the practical “tangible” realities of life, where as number theory all to often can not be expressed in a tangible way no matter what.

It’s why I talk about comparing “Apples with Apples” and why if you can not do that, then your proof no matter how apparently elegant is not anything of the sort. A mistake that is oft made and I oft wish I did not come to my attention.

Cantor’s “diagonal argument” is not in the slightest touched by this because “It works with apples through out”.

But getting to the point of not just knowing this but understanding it in a way that enables further insight is a step few make, or apparently can make. In fact one of the issues we still do not understand from Cantor’s time was “madnesss in mathmaticians”, their early demise, and why there was a strong corelation with certain heriditary groups from the areas of Austria and Hungary of the time.

]]>The size of infinities is infinite

Set theory is fascinating, and I marveled at Cantor’s theory when I first saw it. However, infinites have limited practical value outside mathematics.

The case of finite sequences is much more useful. And the link between computational complexity and probability theory is of real practical value in this.

]]>The size of infinities is infinite

Aleph Naught went to the Hilbert Grand Hotel

She was able to get a room.

hxtps://en.m.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_Grand_Hotel

But, the bar was very crowded.

hxtps://nitter.net/cwsshotboard

]]>However in the infinite string of digits sense all those reals collapse down to the same as the natural numbers, as you would expect.

Cantor also showed that talking about infinite set is very tricky.

I feel not qualified to explain the differences, others have done a good job here. But a fundamental mistake in your reasoning is that the integers are part of an infinite set of *finite* sequences of digits. The reals are a “larger” infinite set of *infinite* sequences of digits.

“What is the difference as far as printing is concerned, of an integer of infinite length and a real of infinite length?”

If you can prove Cantor wrong, prepare yourself for the Fields medal.

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