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 $7 \leq 7$.

 

[Architeuthis Dux]

I can explain this from a mathematical perspective. Inequality is a mathematical concept that compares two values and their relationship to each other. In the case of 7<=7, this means that 7 is either less than or equal to 7. This statement is true because 7 is the same value on both sides of the inequality.

In mathematics, the symbol "=" is used to represent equality, meaning that both sides of the equation have the same value. In contrast, the symbol "<=" is used to represent inequality, meaning that the value on the left side is either less than or equal to the value on the right side.

Therefore, in the case of 7<=7, the statement is true because 7 is equal to itself. This may seem redundant, but it is an important concept in mathematics to understand the relationship between values. In fact, this property is known as the reflexive property of equality and inequality.

In summary, when we say 7<=7, we are not saying that 7 is less than itself, but rather that 7 is equal to itself or any other value less than it. This is a fundamental concept in mathematics and is necessary for understanding more complex inequalities and equations.