Is the product of two numbers both less than one less than one

Question

I'm bad at mathematics, and I wanted to know something.

Say there are two numbers $a$ and $b$ where $a, b \in \Bbb R$ $-1 < a < 1$ and $-1 < b < 1$ Is it necessary that $a \times b < 1$?

Edit: I was in hurry and didn't notice the big mistake I did

score 3 · Accepted Answer · answered Nov 08 '13 at 10:56

3

Yes, because $|ab|=|a||b|<1\cdot 1 = 1$, hence $-1<ab<1$.

answered Nov 08 '13 at 10:56

user106375

score 2 · Answer 2 · answered Nov 08 '13 at 10:46

2

Not necessarily: $$ (-2)\times(-2)=4. $$ It will be true if the two numbers are positive and less than one.

answered Nov 08 '13 at 10:46

Julián Aguirre

I agree with your answer, but I think he meant positive reals. But your answer is correct based on what he supplied. – Rocket Man Nov 08 '13 at 10:47
I read $-1<a<1$ and $-1<b<1$ in the question (probably updated in the grace period, so the edit is not visible in history). – egreg Nov 08 '13 at 11:30

2 Answers2