/sci/ - Science & Math

>professor says something about the sum of to rational numbers is always rational. one of the students asks if he can prove it, and the professor says "no, it's an axiom".
Writing a proof takes literally less than a minute.

Let [math]a, b, c, d \in \mathbb{Z}[/math] where [math]b, d \neq 0[math].

Now, [math]\frac{a}{b} + \frac{c}{d} = \frac{ad}{bd} + \frac{cb}{db} = \frac{ad + cb}{bd}[/math],

which is a rational number since [math]ad + cb \in \mathbb{Z}[/math], [math]bd \in \mathbb{Z}[/math] and [math]bd \neq 0[/math].

There are infinite amount of options. For example, [math]e^0[/math].

[math]0.999... \leq e^0 \leq 1[/math]