Greatest Integer

MathsLearner

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I am self learning maths and trying to solve problems online. I don't understand the wording of the problem "Greatest integer less than or equal to x".
Does it mean if x = 2013 then [x] is 2013 since it is equal to x. Please guide me.
 

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Dr.Peterson

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Nov 12, 2017
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I am self learning maths and trying to solve problems online. I don't understand the wording of the problem "Greatest integer less than or equal to x".
Does it mean if x = 2013 then [x] is 2013 since it is equal to x. Please guide me.
Yes, the greatest integer function (also called the floor function) returns x itself when x is an integer.

So in your problem,
The number of solutions of x + [x] = 2013, where [x] is greatest integer less than or equal to x, is ...
we know that [x] is an integer, so x itself must be an integer, and the equation can be rewritten as x + x = 2013. The answer is easy from there.
 
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