False or true?

Algebra Level 3

For all ordered fields $\mathbb{F}$ , $0_{\mathbb{F}}<1_{\mathbb{F}}$ .

Where $0_{\mathbb{F}}$ is the additive identity and $1_{\mathbb{F}}$ is the multiplicative identity in $\mathbb{F}$ .

Not enough information True Cannot be determined False

1 solution

Ravi Dwivedi
Nov 8, 2019

An ordered field $\mathbb{F}$ is a totally ordered set with a field structure such that for all $a,b,c \in \mathbb{F}$ the following holds:

If $1<0$ then $-1>0$ and by 2 above, we get: $1=(-1)\cdot (-1)>0$ and note that $1\neq 0$ in a field and therefore the conclusion follows.