The List of Undisputable Givens and Laws

[reds4ever]

0 to 9 is just base 10, we can express numbers in any base, base 8 is octal, 16 is hex (0 to 9 and A to E), 2 binary ( 1 and 0)etc

but your right in that that's why it's instintive to multiply by 10

[Ramo]

no, i don't, i know seemingly straight forward proofs were called into question in the eighties, but i don't pretend to understand the math behind it, but YOU prove AB = BA when A and B are real numbers wrong.

I can't. That's part of the definition of real numbers; i.e, they're commutative. I'm just saying that the premise that "A & B are real numbers implies AB = BA" is true if and only if you define real numbers as commutative a priori (if you decide to call matrices "real numbers," the premise isn't true).

Saying "A & B are real numbers implies AB = BA" is indisputable is equivalent to saying that "coffee is caffinated beverage made from coffee beans" is indisputable.

[SnowFire]

I haven't dealt with a prime number in years. Forgive my mental lapse; do prime numbers have to be greater than 1 or 2?

The response already given is on target about having 2 distinct factors, but that's still a definitiony thing. Why not define primes to be numbers with 2 or less factors? How about the number -1? Etc. Primes are usually defined as numbers strictly greater than 1 with only 2 factors.

There are several reasons for this, but probably the best one is the fundamental theorem of algebra. Every number can be uniquely factored into primes, right? Well, if 1 is prime, this isn't true. 6 can be factored into 3*2, or 3*2*1, or 3*2*(1^2), etc. A prime is supposed to be an indivisible building block to build off of; not an identity like 1.

If you ever take Rings & Fields, or possibly Group Theory, you can see this there as well. When running around funky different fields or groups, you will still find a unique identity for the group operation, and in the case of fields, its own primes.

[Ramo]

Ah, thanks.