Help, I'm drowning!! In proofs. I am sooooo lost in this class.
1. Prove that the set of positive real numbers has cardinal number c. (Hint: try the map x --> e^x.
2. Prove that the open unit interval 9the set of all real x with 0 < x < 1) has cardinal number c. (Hint: Use ex. 1 and the map x --> x/(1 + x), defined on all positive real numbers).
3. Whatis the cardinal number of the closed unit interval (all x with 0 < x < 1)? Of the half open interval (all xx with0 < x < 1)?
First show f is injective (one-to-one), then show f is surjective (onto).
Intuitively/geometrically, f being injective means it passes the horizontal line test.
f being surjective means that the codomain equals the image.
Injective, Surjective and Bijective