One such function is [ Y = INT(x) ]. (Y is equal to the greatest integer in ' x ')
Integers never stop. There is no single greatest one.
There are many such functions. For example, any function of the form y = x^a where a is an odd positive integer will do.
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It means that the function value doesn't make sudden jumps. For example, a function that rounds a number down to the closest integer is discontinuous for all integer values; for instance, when x changes from 0.99 to 1, or from 0.999999 to 1, or for any number arbitrarily close to 1 (but less than one) to one, the function value suddenly changes from 0 to 1. At other points, the function is continuous.
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.
There is no greatest integer. Whatever integer you think is greatest, you can always add one (1) to it and get a larger one.
One such function is [ Y = INT(x) ]. (Y is equal to the greatest integer in ' x ')
You cannot, because there is no greatest integer. If you thought you had one, then move just one unit to the right and you will have an integer which is greater.
No. For any integer, you can add one to get an even greater integer.
Integers never stop. There is no single greatest one.
Perhaps it makes sense to ask; in any case, the answer is that there is no greatest and no smallest integer. Whatever number you choose, you can always add one to get an even larger integer; or subtract one to get an even smaller one.
The way the number line is usually drawn, the greatest integer is the one that is to the right of all the others.
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
There are many such functions. For example, any function of the form y = x^a where a is an odd positive integer will do.
No. The positive integers are {1, 2, 3, 4, 5, ...}. They start at 1 (which is the least positive integer) and progress forever (to infinity). There is no end to the positive integers, so there is no greatest positive integer. Another way to look at it might be to think of any really large integer (a "counting" or "whole" number) and add one. That will create a "next bigger" large number. You can continue to do this infinitely many times.