The goal of this exercise is to prove the following theorem in
several steps.
Theorem: Let ? and ? be natural numbers. Then, there exist
unique
integers ? and ? such that ? = ?? + ? and 0 ≤ ? < ?.
Recall: that ? is called the quotient and ? the remainder of the
division
of ? by ?.
(a) Let ?, ? ∈ Z with 0 ≤ ? < ?. Prove that ? divides ? if and...
Use the Intermediate Value Theorem and the Mean Value Theorem to
prove that the equation cos (x) = -10x has exactly one real
root.
Not permitted to use words like "Nope", "Why?", or
"aerkewmwrt".
Will be glad if you can help me with this question, will
like to add some of your points to the one I have already summed
up.. Thanks
Explain what it is a neutral theorem
in Euclidean geometry.
State & prove both: the theorem on construction of parallel
lines and its converse. Which one of them is neutral?