Prove that set of all rational numbers is countable

This claim is proven by building a bijection by following a diagonal procedure.

Imagine you have an infinite matrix, whose coefficient are all possible fractions:

Now, count them "diagonally": this is how we map every natural number, using the same positions:

The attached image, taken from aminsaied.wordpress.com/2012/05/21/diagonal-arguments/, should make it clearer

associative property hopes this ! : )

step-by-step explanation:

fa tha first one you gonna add y to both sides

it look like this

x-y+y=6+y

x=y+6

therefore your answer is

x =y+6

fa tha second one

you gonna flip tha equation

it gonna look like x-4y=y

then add 4 to both sides

it gonna look like tha

x-4 +4 =y +4

so therefore tha answer is x=y+4

step-by-step explanation: