would this be a correct proof of the cauchy-schwartz inequality:

Question

abs=absolute value
abs(u*v) is less than or equal to abs(u)*abs(v).
Then you divide both sides by abs(u)*abs(v) so that you get cos(theta) is less than or equal to 1.

Answer 1

If you know that the dot product of vectors u and v is |u| |v| cos theta
then you can surely say that
u dot v </= |u| |v|