Question

Math using a different numeral system

Answer 1

It’s the same try it!

Answer 2

How we write numbers is just a form to represent what is meant (ie 6 is the number that is 1 bigger than 5 and 0 being the "anchor" to fix all of these recursive definitions) so any other number system would work the same way.

Also, the change of base system is, what mathematicians call an isomorphism, a 1-to-1 correspondence that respects operations as in, it doesn't matter if I switch number systems and then perform an operation or do the operation first and then switch number systems.

Answer 3

Do you agree that "6", "six" and "VI" are the same number? They represent the same thing, after all.

In much the same way, "6+3=9", "six plus three is nine" and "VI+III=IX" are all the same equation, just with a different look. They all *mean* the same thing, though. Even though the number systems don't even have the same structure! One is a positional notational system, one is based on words, and one is based on god knows what the Romans were thinking when they invented that. Still, the algebra is the same because all three systems are used to represent something more overarching, more abstract: numbers are something with inherent meaning, they're not just a string of symbols. Algebra is about numbers, not about their representations on paper or on a screen. So the algebra doesn't change when changing the number system, even if the systems bear no resemblance at all. And the same is doubly true for number systems which are structurally similar, like a base 10 and a base 11 system.

Answer 4

Let me ask you something first: do *you* think it would? And if so, why do you think that? It can be a guess or a hunch, I just wanna know your thinking on this

Answer 5

Algebra is the same in binary or decimal

Answer 6

In base 12, ninety is 76 (in decimal, 90 = 7x12+6). The sum of the “digits” in base 12 is 7+6=11 (in decimal, 7+6 = 13 = 1x12+1). But 11 isn’t divisible by 9. So, we lose the sum of digits rule for divisibility of 9, and those there are some things that are dependent upon base, in number theory in particular.

(I believe in general, the sum of digits rule works for base-1. We are just to thinking of it for 9 because we use base 10 almost exclusively.)

Note: 11 isn’t divisible by 9 in base 12 or base 10. However, 11 is divisible by 9 in base 17. In base 17, the numeral 11 represents the same number as 18 in decimal, namely “eighteen”. I intentionally wrote out the word “ninety” above to avoid such confusion, but at this point, I’m just being silly.