Question

f(m,n) = m^2 – n^2 is onto or not kindly tell me with detail because i don't understand how ?

Answer 1

onto what?

Answer 2

lets say the function is ZxZ -> Z

Answer 3

f(m,n) is onto if for each element of y of Z there exists (m,n) of ZxZ such that f(m,n) = y

Answer 4

so it is not onto if you can find some number such that f(m,n) is never equal to y . what about y = 2. is the difference of two squares ever equal to 2?

Answer 5

also i am assuming, m,n are integers

Answer 6

So in \(\mathbb{R}\) yes but not in \(\mathbb{Q}, \text{ or } \mathbb{Z} \)

Answer 7

right, it depends on what the domain and codomain are.

Answer 8

how do you type R in latex?

Answer 9

without going into the equation editor

Answer 10

normally at lower level we only talk about the real line, so if this is for something a little more advanced I am surprised the OP did not specify that set...

Answer 11

`\(\mathbb{R}\)`

Answer 12

\(\mathbb{R}\)

Answer 13

:)

Answer 14

how did you get that in grey?

Answer 15

hmm I dont know if i can type it

put a ` at the start of your code, and ` at the end

Answer 16

hmm

Answer 17

a\(\mathbb{R}\)a

Answer 18

put the thing under ~ at the start of your code and the thing under ~ at the end

Answer 19

zzrock, can you help me with my question, sorry i dont mean to be rude

Answer 20

i am snatching you :)

Answer 21

`\(\mathbb{R}\)`

Answer 22

its basic algebra

Answer 23

if I can, sure where is it?

Answer 24

http://openstudy.com/study#/updates/537ff745e4b04df7f20841e5