Why is 7 less than or equal to 7 in inequality math?

[Nikolas15]

Homework Statement

Basically I was reviewing a proof of one of the inequality properties and there was a statement that a <= a , or in other words for ex. 7<=7. So my question is why is that, since 7 is really = to 7, at least I think so.

thanks.

 

[jgens]

The sign $\leq$ mean less than or equal to. So saying $7 \leq 7$ means that $7$ is less than or equal to $7$. Now, in mathematics (and pretty much everywhere else) the word "or" means that either one or the other holds (and depending on the context, potentially both). Clearly $7 < 7$ is absurd, but $7 = 7$ is true which means that one of the two clauses holds, thus $7 \leq 7$.