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
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.
Less than
Neither of the two are one-to-one
Inverse of a function exists only if it is a Bijection. Bijection=Injection(one to one)+surjection (onto) function.
piecewise
-51
The greatest integer function, often denoted as ⌊x⌋, gives the largest integer less than or equal to x. For 0.7, the greatest integer is 0, since 0 is the largest integer that is less than or equal to 0.7. Thus, ⌊0.7⌋ = 0.
No. It has a discontinuity at every integer value.
Yes, the greatest integer function, often denoted as ⌊x⌋, is many-to-one. This means that multiple input values can produce the same output. For example, both 2.3 and 2.9 yield an output of 2 when passed through the greatest integer function, as both round down to the greatest integer less than or equal to the input. Thus, it is not a one-to-one function.
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.
Less than
Neither of the two are one-to-one
yes
The greatest integer function, often denoted as (\lfloor x \rfloor), returns the largest integer that is less than or equal to the given value (x). For example, (\lfloor 3.7 \rfloor) equals 3, while (\lfloor -2.3 \rfloor) equals -3. This function effectively "rounds down" any non-integer value to the nearest whole number.
Inverse of a function exists only if it is a Bijection. Bijection=Injection(one to one)+surjection (onto) function.
piecewise
No, because there is no greatest integer.