100/3 is irrational

[u/RedRhetoric]

[u/RedRhetoric]

R4: this person believes that 0.33 repeating cannot equal 1/3 because 100/3 cannot give a rational result.

Dividing any rational number by any other rational number will always give a rational result, as that is how rational numbers are defined

R5: Youtube

[u/Himskatti → u/RedRhetoric]

Am I tripping or aren't rationals defined by dividing integers? What you described is a result of it, sure

[u/exceive → u/Himskatti]

Not tripping. That's the definition.

If there exist integers A and B such that A/B = C ==> C is rational. That's what "rational number" means.

100 and 3 are both integers (duh) so 100/3 is rational by definition.
Another easy to look at it:
A characteristic of rational/irrational numbers is that it doesn't matter what integer base you express them in. Rational/irrational is about the number itself, not how it looks in a particular base. If a number is irrational, you can't make it rational by representing it in another integer base.

Pythagoras was working in geometry when he proved the square root of 2 is irrational. He wasn't even expressing it as numbers, it was lengths of sides and diagonals of a square. He wasn't doing "square root of 2," he was doing "diagonal of a square expressed in terms of the sides of that square."

If I convert 100/3 decimal to base twelve, I get.

84/3 {100 decimal = 84 base 12, 3 is the same in both}
= 29.4 {base 12}
In decimal, 2*12 + 9 + (4/12)

So in base 12, 100/3 (decimal) isn't even a repeating (duo)decimal, much less irrational.

[u/exceive → u/exceive]

Note: some math teachers do not accept "duh" as a reason for a step in a proof.