Pillah wrote:

does anyone know what [x] means?

eg: If [x] denotes the greatest integer less than or equal to x, is [x] = 0

I'm having trouble understanding what If [x] denotes the greatest integer less than or equal to x means

Every real number can be placed between two consecutive integers, such that \(k\leq{x}<k+1\).

For every given \(x\), the integer \(k\)with the above property is unique. By definition, then \([x] = k\).

You can always write \([x]\leq{x}<[x]+1.\)

If \(x=5,\) \([5]=5\). If \(x=5.67\), \([x]=5.\)

\([0]=0\), \([0.84]=0\), but \([-0.34]=-1.\)

If \(x\) is an integer, than \([x]\) is simply \(x.\)

For non-integer \(x\), try to visualize the number line. The closest integer to \(x\) from the left is \([x].\)

We used to call it

the integer part function. For positive numbers, just ignore the decimal part and leave the integer part of the number.

For negative numbers, don't forget to look at the left of your number. \([-2.7] = -3\) and not \(-2.\)

So, if \([x] = 0\), then certainly \(0\leq{x}<1\), meaning \(x\) can be any number between 0 and 1, 0 inclusive, 1 exclusive.

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PhD in Applied Mathematics

Love GMAT Quant questions and running.