Going from to is incorrect. You forgot to square the 2.
Hello please could you tell me if my proof that the sqrt of 4 is irrational is correct.
therefore so ....1.1
This implies that a is greater than b and that a is even.
a is even so a=2k
put into 1.1
cancel by 4
this can be written as this implies that which implies that ....1.2
Equation 1.2 contradicts equation 1.1. This shows that a and b cannot be whole positive integers.
I think I've proved it is rational.
a^2=4b^2 = 2b=a
Because we have proved a is an even number, b also must be even
Because a is greater than b and they are both integers we know it cannot be a decimal and we know that if a number can be written as a fraction then it is rational. Because they are both even it can be written as a fraction.
Q.E.D
Ah, you're right, didn't think of that. In fact it's true that . Misinterpretation on my part.
Edit: Actually, I'm wondering whether this is normal syntax for the "=" sign, or for equations containing an unknown.
Edit 2: I think the syntax is perfectly valid, after a little thought. I don't think anyone would have a problem with this statement:
Then in the context of solving equations, we have, for example
Contrasted with