<= vs < when proving big-o notation

Posted by user600197 on Stack Overflow See other posts from Stack Overflow or by user600197
Published on 2011-02-02T15:24:46Z Indexed on 2011/02/02 15:25 UTC
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We just started learning big-o in class. I understand the general concept that f(x) is big-o of g(x) if there exists two constants c,k such that for all x>k |f(x)|<=c|g(x)|. I had a question whether or not it is required that we include the <= to sign or whether it is just sufficient to put the < sign?

For example: suppose f(x)=17x+11 and we are to prove that this is O(x^2). Then if we take c=28 and x>k=1 we know that 17x+11<=28x^2. So since we know that x will always be greater than 1 this implies that 28x^2 will always be greater than 17x+11. So, do we really need to include the equal sign (<=) or is it okay if we just write (<)?

Thanks in advance.

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