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None if n > m

n! if n = m

and

mPn = m!/(m-n)! where k! denotes 1*2*...*k

Q: How many one one functions are defined from a set having n elements to a set having m elements?

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2x2^(n-2)

8 sets of 6 elements would have 96 elements (8X6=96)

No. There are many common functions which are not discrete but the are not continuous everywhere. For example, 1/x is not continuous at x = 0 (it is not even defined there. Then there are curves with step jumps.

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By ordering the digits, you can make 4*3*2*1 = 24 different numbers. By using mathematical operations that are already defined (addition, power, trigonometric functions etc), you can make many more - at least millions. If you then include functions that you define, the answer is infinitely many.

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2x2^(n-2)

8 sets of 6 elements would have 96 elements (8X6=96)

No. There are many common functions which are not discrete but the are not continuous everywhere. For example, 1/x is not continuous at x = 0 (it is not even defined there. Then there are curves with step jumps.

A line segment can be defined as having two endpoints

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None. There must be at least one example of a many-to-one mapping.

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