Four typo's/grammer errors in chapter 10

[VincentdeJager]

Dear,

While reading your online book, I've come across four typing errors in chapter 10.

On page 3 you wrote ''the'' two times in a row: "The second hidden unit can compute an “and” function: x1 ^ x2. The the output can combine these into a single prediction that mimics XOR."

on page 10, there are two errors in one sentence, appointed between brackets. the sentence is: "This is a very famous result because it shows that constant-depth circuits are less powerful that [should this be 'than', not 'that'?] deep circuits. Although a neural network isn’t exactly the same as a circuit, the [the what? a word is missing here] is generally believed that the same result holds for neural networks.

And secondly, on page 12 there are 2 times ''the'' after each other. "The gradient terms for v remain unchanged from before, the the derivates for the other variables differ."