Cantor’s Mistake

Devans99 January 03, 2020 at 18:49 3025 views 8 comments

Cantor thought that he could measure something that has no size. He looked at the infinity of the natural numbers and noted it follows a particular pattern. He called that pattern aleph-zero, claimed it was a number and that it was possible to do arithmetic with it. He then proceeded to examine the infinity of reals, noted that they cannot be put into one-to-one correspondence with the naturals hence had a different fundamental pattern.

What Cantor was doing was identifying patterns or the organisation of the abstract structures formed in our minds by different types of infinity. Patterns are not sizes/cardinalities/numbers. It is, in general, not possible to do arithmetic with patterns. What is a snowflake plus one? What is a hexagon times a snowflake? - nonsensical questions.

Infinity is just an abstract concept that exists in our minds. It takes two different organisations/patterns (that of the natural and the reals). It is not measurable because it conceptually goes on forever. It has no size/cardinality because it is unmeasurable. Cantor identified that there are two different such abstract structures with different patterns/layouts. That is the sum of his legacy and no more.

Comments (8)

aletheist January 03, 2020 at 18:56 #368176 0 likes

Reply to Devans99
The thread title should be "Devans99's Mistake." Your constant grinding of this particular ax became tiresome long ago. Saying the same thing over and over, and expecting a different result, is one definition of insanity.

Devans99 January 03, 2020 at 18:57 #368177 0 likes

Reply to aletheist Thats not a counter argument.

aletheist January 03, 2020 at 19:04 #368179 0 likes

Reply to Devans99
Brilliant insight! You have amply demonstrated in other threads that you are not interested in counter arguments. Your mind is already firmly made up that reality is entirely discrete and finite, and any approach to mathematics that is not consistent with this dogmatic assumption is to be discarded.

Devans99 January 03, 2020 at 19:08 #368181 0 likes

Reply to aletheist I am open to counter arguments. Thats why I post here. To get other people's ideas and counter arguments. I have not made up my mind that space is finite and discrete; I merely think there is an approximately 80% chance that is the case, I await further arguments / counter arguments to hone that estimate.

unenlightened January 03, 2020 at 21:12 #368200 0 likes

Quoting Devans99

I have not made up my mind that space is finite and discrete

This is entirely to be recommended. I too like to make my ideas conform to reality rather than try to argue reality into conforming with my ideas.

ssu January 03, 2020 at 21:25 #368207 0 likes

Quoting Devans99

Infinity is just an abstract concept that exists in our minds.

Infinity is quite useful in mathematics. Doesn't everything in math exist in our minds?

Quoting Devans99

He looked at the infinity of the natural numbers and noted it follows a particular pattern. He called that pattern aleph-zero, claimed it was a number and that it was possible to do arithmetic with it. He then proceeded to examine the infinity of reals, noted that they cannot be put into one-to-one correspondence with the naturals hence had a different fundamental pattern.

Yes, what does it indeed mean? What is the thing that transcendental numbers bring to this? It's a great question.

Deleted User January 03, 2020 at 22:31 #368220 0 likes

This user has been deleted and all their posts removed.

Streetlight January 03, 2020 at 22:40 #368221 0 likes

There are enough threads going on Cantor and mathematical infinity right now with active discussion, we do not need another.