Assume that f : \mathbb{n} → \mathbb{n} and defined by f(n) = n - 1 for all n > 0 and f(0) = 0.
prove in this case that the function g : p(\mathbb{n}) → p(\mathbb{n}) is injective.
describe the sets g[{0,1,}], g[\mathbb{n}] and g[\mathbb{n} \ {0}].
is the function g surjective? show why.

Hiroaki wants to find 3 3/4 - 7/8 explain why he must rename 3 3/4 to do the subtraction.

Martha has a deck of cards. she has lost some of the cards, and now the deck only contains nine spades, eleven diamonds, eight clubs, and twelve hearts. martha predicts that whenever she draws a card from the deck without looking, she will draw a club one-fifth of the time. which activity would best allow martha to test her prediction? a. randomly draw a card from the box and see if it is a club. b. randomly draw a card. then, continue to draw another card until all eight clubs are drawn. c. randomly draw and replace a card 120 times. then, observe how close to 30 times a club is drawn. d. randomly draw and replace a card 100 times. then, observe how close to 20 times a club is drawn.

Aculture started with 4,000 bacteria. after 5 hours, it grew to 5,200 bacteria. predict how many bacteria will be present after 19 hours. round your answer to the nearest whole number.