Let A and B be two mon-empty sets and let f A - B be a function. Define a relation a ~ 6 for a. b €
A by a 6if and only if f(a) = f(b)
show that a ~b is an equivalence relation
Describe corresponding equivalency classes
If f is injective, how many representatives do ench equivalency class have?
Show that h is a contractual image on R
Given an arbitrary pointp € R and let P1 = h(p),P2 = h(p2).Ps = h(p2) etc, ie Pn = hT.show that
Assume that the functionf (0,00) - (0, bo) is continuous and decreasing. Show that limit
exists. (Tip: that monotonous and limited numbers of resal numbers are convergent, may be used without
These solutions may offer step-by-step problem-solving explanations or good writing examples that include modern styles of formatting and construction
of bibliographies out of text citations and references. Students may use these solutions for personal skill-building and practice.
Unethical use is strictly forbidden.