so what plato means here is it just depends on how in depth you want to proof it right?? so Jhevon answer is not wrong right?? I just don't get it b/a is also a rational number right?
no it is not wrong, it is just incomplete--i basically just did the steps, but you may be required to show how and why those steps work, and why is it valid for me to do what i did.so Jhevon answer is not wrong right??look at how we defined a rational number. it is a fraction made up of two integers where the bottom integer is not zero, doesn't b/a have that property as we defined it?I just don't get it b/a is also a rational number right?
yeah I get all that, because of x cannot be equal to 0 therefore a cannot be 0 and b also can't be 0 since the first time it is stated. So b/a is still a rational number although it is flipped.
though there is still another question that I am willing to do but I just need some hints:
If n is a perfect square, then n+2 is not a perfect square.
Here's what I've did so far:
The definition of a perfect square is:
An integer a is a perfect square if there is an integer b such that
Therefore in this question:
= is a perfect square but because you add 4 to it, it doesn't become a perfect square again
therefore it's not a perfect square?
is this right?
By factorization we have that . Impossible*
*)The cool way of saying is that the integers form a unique factorization domain. Which basically is the Fundamental Theorem of Arithmetic is that we can factorize the integers > 1 uniquly.
also one more thing is that I am only asked to do this whether by direct proof or contraposition.
If I use direct proof, thereforeL
is not a perfect square right? because you can't factor it?
is this right if I am trying to proof this using direct proof?