Recent content by kaos

Well i don't really know how to use the hint. But anyway its been explained in my online course how to prove it using the fact that sqrt of 2 and 3 are irrational, and using it to generalise it to primes( we did the proofs for sqrt of 2 and 3 earlier in the course). Thanks for the help guys ,its...

I think its obvious that a prime number can't be a square of an integer (trivial by definition), but that does not imply it cannot be a square of a rational. The thing I am trying to prove is that the square root of primes ,is not rational. Am i misunderstanding the logic ,overlooking or...

Homework Statement Im trying to prove that if p is prime, then its square root is irrational. The Attempt at a Solution Is a proof by contradiction a good way to do this? All i can think of is suppose p is prime and √p is a/b, p= (a^2)/ (b^2) Is there any property i can...

Ah right i confused naturals(whole numbers larger than zero) with integers (integers include less than zero whole number right). Thanks for the explanation.

Yes i know of proof by contradiction, but i used a more straightforward method. Though I am not entirely sure my proof works.

Thanks for responding. Isn't the square of an integer always different?(except 1 or 0 i guess)? And I don't understand the "(You need to argue that in order to know that squaring does not cause everything to collapse into a small, finite set of values.)" part (specifically what are you...

Is this a valid proof? Also is this way of doing it valid? Statement : There are infinitely many natural numbers n where the square root of n is rational. Proof: sqrt of n = x (where x is natural) n= x squared And n can be any natural number(x) squared ,and there are...

Thanks Dick and Hallsofivy.

Ah ok i see , thanks guys.

Is this proof valid? Suppose 5r is rational 5r is p/q (p and q are intergers with no common factors) r= p/5q p and q are integers and 5 is an integer , and 5q is an integer since integers multiplied by intergers are always integers. Since the r= integers/ integers , r is a rational...

If i construct a rational in between p/q and r/s , i doesn't apply to any other rationals, so it doesn't really prove anything. Am i misinterpreting your statement ( I am really bad at math so please excuse my lack of ability)?

Can someone check if my proof is correct.Please exscuse the bad notation, I've no idea how to type the symbols. The question was prove that between any 2 rational number , there is a third rational. x,y ,z are elements of Q (for all x ) (for all y) (there exist z)[x>z>y] <-> (for all x ) (for...

Is this proof valid? I seen this proof from my study group in this course: if r + 3 is rational, then r is rational assume r + 3 is rational. then r + 3 can be expressed as follows r+3=p/q where p and q are integers subtract 3 from both sides r=p/q−3=(p−3q)/q p - 3q (since q is an...

Thanks Dick , your help is much appreciated.

Well I am not sure that there could be other types of number other than rational or irrational, which is why i asked. In other words I am not sure that (~rational implies irrational). Is it valid to say that ~rational if and only if irrational and ~irrational if and only if rational? If i...