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:
-1 5/36
Step-by-step explanation:
Answer:
ok
Step-by-step explanation:
yeah
Answer:
{x\ x e U and x has a negative square root} is an empty set.
Step-by-step explanation:
If x e U, x is a negative real number, and they don't have a square root (they don't have even roots). Their square roots are complex numbers, not real ones.
Answer:
88.83
Step-by-step explanation:
To find the mean of a set of numbers is to find the average a set of numbers.
To solve for the mean you have to add all of the values together and divide that sum by the number of values there are.
Ex. 81, 97, 99, 89, 91, 76
81 + 97 + 99 + 89 + 91 + 76 = 533
533 / 6 = 88.83
↓
(number of values)
