Just wondering if anyone could confirm if I've headed in the right direction with these
(a) Prove the triangular inequality: |x + y| ≤ |x| + |y|.
(b) Use triangular inequality to prove |x − y| ≥ ||x| − |y||.
(c) Show that if |x − a| < c/2 and |y − b| < c/2 then |(x + y) − (a + b)| < c.
So for...
Thank you! I'm a little stumped on part (b) and (c), so from what I understand injection means we have to show how it is a one-to-one function that is h(f(x)) has one value of x=X for every y=Y?
Okay, thank you! Also in regards to (a) - would it be looking somewhat like this?
So if we suppose that f is a surjection. We define a function g : Y → X as follows.
Let y ∈ Y , and since f is a surjection, there exists x ∈ X (not necessarily unique) such that f(x) = y.
Now we choose one such x...
Hmm I think I kind of get the idea. Do you happen to know where I could potentially read more about this topic that uses examples like you've provided? I think I generally understand theories and proofs better when looking at a specific example then taking from that to understand the...
Just wondering if anyone could help me get in the right direction with these questions and/or point me to some material that will help me better understand how to approach these questions
In what follows I will denote the identity function; i.e. I(x) = x for all x ∈ R.
(a) Show that a function...
Ahh thank you for the pointer! First time posting so will keep that in mind. Will post my working out so far in the morning, also will repost this in the homework type question forum as I just read that these types of questions are best directed there.
Stumped on a couple of questions, if anyone could help!
In what follows I will denote the identity function; i.e. I(x) = x for all x ∈ R.
(a) Show that a function f is surjective if and only if there exists a function g such that f ◦ g = I.
(b) Show that a function f is injective if and only if...