Marco Rovere (3) [Avatar] Offline
#1
Hi,
assuming that you are interested in a function (bijective) that is mapping 10 different integers into other 10 different integers, I'd argue that the correct answer is 10!, not 10^10.
Nishant Shukla (52) [Avatar] Offline
#2
You're right if we assume the function must be bijective.

But the reason we don't assume it to be bijective is because that's rarely the case in machine learning applications. For example, in classification the domain of the function can be huge compared to the co-domain (think about a 32x32 image as input, and 2 classes as output).
479593 (2) [Avatar] Offline
#3
I was going to create a thread for Exercise 3.1 but found this. I believe the answer should be "infinite number of functions". Even if we add the following constraint

f(i) = i, for i = 0, ..., 9

The answer is still "infinite number of functions". You are infinite number of possible values to map to in between.
479593 (2) [Avatar] Offline
#4
I think what you were really asking is permutation with replacement not function. Function defines a map from a set of inputs to a set of permissible outputs. If you want to make the answer 10^10, you have to add that the function is solely defined over {0, 1, ..., 9}