Answer:
Consider f: N → N defined by f(0)=0 and f(n)=n-1 for all n>0.
Step-by-step explanation:
First we will prove that f is surjective. Let y∈N be any natural number. Define x as the number x=y+1. Then x∈N, and f(x)=x-1=(y+1)-1=y. We conclude that f is surjective.
However, f is not injective. Take x1=0 and x2=1. Then x1≠x2 but f(x1)=0 and f(x2)=x2-1=1-1=0. We have shown that there are two natural numbers x1,x2 such that x1≠x2 but f(x1)=f(x2), that is, f is not injective.
Note:
If 0∉N in your definition of natural numbers, the same reasoning works with the function f: N → N defined by f(1)=1 and f(n)=n-1 for all n>1. The only difference is that you consider x1=1, x2=2 for the injectivity.
Answer:
20, 35, 50
Step-by-step explanation:
Answer:
Step-by-step explaA bag of marbles contains only purple and yellow marbles. The bag has three times as many yellow marbles as purple. The bag contains 164 total marbles. Write an equation or system of equations to find out how many of each color of marble is in the bag. Define your variable(s) and expressions. Show how you checked your answer.
2nation:
Answer:
(3,4) and (6,8).
Step-by-step explanation:
Rise is equal to y and run is equal to x. If the fraction is 4/3, y is equal to 4 and 3 is equal to x. 3 across is 3 and 4 upwards is 4. Just keep adding 3,4 to get the following points the line passes through. Since we need two points, 3,4 and 6,8 would be the appropriate answers.
To create a line that is perpendicular to the one given, completely invert the slope.
y = -3/2x + 9
