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I'm taking the free Caltech machine learning course. I'm having trouble understanding the notation on one of the problems:

In this problem, you will create your own target function f and data set D to see how the Perceptron Learning Algorithm works. Take d = 2 so you can visualize the problem, and assume X = [−1, 1] × [−1, 1] with uniform probability of picking each x ∈ X .

What does it mean that X = [−1, 1] × [−1, 1] ? what does the x or times symbol mean? Is this a continuous range or discrete set of elements? Basically what values can be in X?

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X consists of all elements $$x = (x_1, x_2) $$ such that $$x_1 , x_2 \in [-1,1]$$ That is $$ -1 \le x_i \le 1$$ for $i = 1,2$

You should consider taking a course in calculus.

The 'x' is the notation for a product space.

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  • $\begingroup$ Can you elaborate on the notation for a 'product space', what that is, and an example of the operation and its result? $\endgroup$
    – Ben G
    Oct 31, 2023 at 0:50
  • $\begingroup$ See en.m.wikipedia.org/wiki/Cartesian_product . Cartesian Product might have been a better description. $\endgroup$
    – ChrisL
    Oct 31, 2023 at 8:49
  • $\begingroup$ oh cartesian product, got it $\endgroup$
    – Ben G
    Nov 1, 2023 at 2:14

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