This is a really basic question that I don't know why I'm not getting. So from my understanding, a=b is defined as a=>b and b=>a.(adsbygoogle = window.adsbygoogle || []).push({});

So say a^2=c and a=c^(1/2)

so which implies which?

Say I start from a=c^(1/2)

I square both sides and I get a^2=c. So a=c^(1/2) => a^2=c.

But if I start from a^2=c, by taking the square root of both sides, I get a=c^(1/2) & -c^(1/2)

But since I got a=c^(1/2) among one of them, I have shown that a=c^(1/2) is still implied by a^2=c.

So a^2=c <=> a=c^(1/2)

Which is clearly not true. they are not the same b/c by taking the square root of both sides we get a=+ or -c^(1/2). Is there something wrong with my reasoning?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Confused about the difference between equivalence and implication

**Physics Forums | Science Articles, Homework Help, Discussion**