/sci/ - Science & Math » Thread #14036289

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Anonymous Fri 31 Dec 01:49:31 2021 No.14036289 View Reply Original Report

Quoted By: >>14036322 >>14036350 >>14036402

Wait, so mathematicians actually believe that there are the same number of natural numbers as integers?
How does that make any sense?
At a distance of 2 from 0 there are integers -2, -1, 0, 1 and 2, and at a distance of 2 from 0 there are natural numbers 0, 1 and 2.
If we extend the number line to infinity in both directions and count what's there, we can clearly see that there is almost double the number of integers as natural numbers.
What are mathematicians smoking?
Have so many been so blind for so long?

https://youtu.be/Zb-RVIETRCE?t=76

Anonymous

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Anonymous Fri 31 Dec 2021 01:55:27 No.14036299 Report

Quoted By:

classic non mathematician not doing the reading and missing common subtleties, like correctly differentiating between *cardinality* and *measure*. Stay unedified, retard. also saged

Anonymous

Anonymous Fri 31 Dec 2021 02:02:46 No.14036322 Report

Quoted By: >>14036350

>>14036289
The natural numbers have a 1-to-1 mapping onto the integers and vice versa. In the same way, the natural numbers have a 1-to-1 mapping onto the odds. Are there the same number of natural numbers as odd numbers?

Anonymous

Anonymous Fri 31 Dec 2021 02:07:02 No.14036326 Report

Quoted By:

It's not true. They all have unique cardinalities.

Anonymous

Anonymous Fri 31 Dec 2021 02:21:48 No.14036350 Report

Quoted By:

>>14036289
Size in the normal sense is undefined, however as >>14036322 points out, a bijective mapping for any finite set recovers the usual notion of size. Hence it allows one to have a "size" for infinite sets despite the unintuitive results.

Anonymous

Anonymous Fri 31 Dec 2021 02:44:55 No.14036402 Report

Quoted By:

>>14036289
I prefer believing they are the same thing, rather than believing that "there are the same number of natural numbers as integers."

It helps with the mental gymnastics.

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