/sci/ - Science & Math

>>11574283
>in the number system we use on a daily basis

Nobody uses real numbers on a daily basis.

Computers natively use a quirky version of whole numbers, and can be taught to use floating point numbers that resemble the set of Rationals numbers up to a point.

But ask a computer to calculate an irrational number and it will invariably stop. If it doesn't run out of memory, it will run out of some other finite resource.

Many things about numbers in computers are utterly incompatible with the real set:

Negative Zero
Machine infinity
Largest and smallest possible numbers. (Both positive and negative.)
Many (most?) numbers do not change when one is added to them, due to exponential notation.

And it is not just computers. If you have two halves of cell phones, you do NOT have a working phone. And I already mentioned half of an electron. And no one ever USED more than 12 digits of Pi to calculate an actual circle. (As opposed to doing it to test math itself.).

The volume of the universe is 4.6×10^185 cubic Planck lengths. Any number larger then this is as meaningless as 0/0.

...So claiming that the Real set is somehow the only set that matters is nonsense. It is just the only set that gives the answer you want.

>>11574283
>If you want 0.999... to not be 1, define your own number system, but good luck making that as free of contradictions as the Reals.

This has been done at least three times:
Surreal numbers
Hyperreal numbers
Base Infinity:

.999... = 1®-1
...999. = 1;-1®
.000...1 = ®1

Numberphile:
https://www.youtube.com/watch?v=WYijIV5JrKg

>>8782098