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:
Step-by-step explanation:
Well, a series in math is simply the sum of the various numbers, or elements of a sequence. For example, to make a series from the sequence of the first five positive integers 1, 2, 3, 4, 5, just add them up. So, 1 + 2 + 3 + 4 + 5 = 15 is a series.
that all what i know i am really sorry bro but that is what i understand !
Answer:
A change in a species that helps it survive
Step-by-step explanation:
i took life science in 7th grade, and another word for this is a mutation (kinda... pls dont make me go there...)
8-5=-3 It's negative 3 because the 8 is greater than 5
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Answer with explanation:</h2>
In statistics, The Type II error occurs when the null hypothesis is false, but fails to be rejected.
Given : Suppose the null hypothesis, 
, is: Darrell has enough money in his bank account to purchase a new television.
Then , Type II error in this scenario will be when the null hypothesis is false, but fails to be rejected.
i.e. Darrell has not enough money in his bank account to purchase a new television but fails to be rejected.
