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Inequality math troubles

  1. Jan 24, 2010 #1
    1. The problem statement, all variables and given/known data

    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.
     
  2. jcsd
  3. Jan 24, 2010 #2

    jgens

    User Avatar
    Gold Member

    Re: inequality

    The sign [itex]\leq[/itex] mean less than or equal to. So saying [itex]7 \leq 7[/itex] means that [itex]7[/itex] is less than or equal to [itex]7[/itex]. 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 [itex]7 < 7[/itex] is absurd, but [itex]7 = 7[/itex] is true which means that one of the two clauses holds, thus [itex]7 \leq 7[/itex].
     
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