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Both the Greatest Integer Function and the Absolute Value Function are considered Piece-Wise Defined Functions. This implies that the function was put together using parts from other functions.
piecewise
-51
No. It has a discontinuity at every integer value.
Less than
Neither of the two are one-to-one
yes
The absolute value of an integer is the integer with no sign. The absolute value of +3 and -3 is 3.
Inverse of a function exists only if it is a Bijection. Bijection=Injection(one to one)+surjection (onto) function.
This function rounds any number down to the nearest integer. Let's use the notation GIF[x]for this site to mean greatest integer function of x. Another name for it is the floor function. So here are some examples: GIF[.9]=0 GIF[1.9]=1 Gif[-1.8]=-2 Here is one trick GIF[1.99999 where 9 repeats forever]=2 (I can not put the bar over it, but usually it would be written as 1.9 with a bar over the 9) The reason is that 1.999999999 forever is =2 so GIF[2]=2
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An odd monomial is an expression of the form axp where a is a numerical constant and p is an odd integer. As a reult of p being an odd integer, a(-x)p = - axp which makes the expression odd.