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

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In inequality math, the expression 7 ≤ 7 indicates that 7 is either less than or equal to 7. The "or" in this context allows for both possibilities to be considered true. While 7 < 7 is false, the statement 7 = 7 is true, satisfying the condition for the inequality. Therefore, 7 ≤ 7 is valid because at least one part of the inequality holds true. This illustrates the fundamental principle that inequalities can include equalities.
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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.
 
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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 &lt; 7 is absurd, but 7 = 7 is true which means that one of the two clauses holds, thus 7 \leq 7.
 

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