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.
956.25 is the answer
Because 1 bottle is 212.5 grams of sugar you can just multiply that by 4.5 because there are 4 bottles and a half of a bottle
Answer:
no
Step-by-step explanation:
I calculated
1 yard = 3 feet
2.5×18=45 feet
45÷3= 15 yards
Answer:
x = 1.5
Step-by-step explanation:
We just have to find the x-coordinate of the point of intersection between the two functions. From the graph, they intersect at (1.5, 2) so the answer is 1.5.
