Why-i-0-and-i-0-

Question Number 9530 by geovane10math last updated on 12/Dec/16

Why i ≯ 0 and i ≮ 0 ? ? ? ?

Commented by geovane10math last updated on 14/Dec/16

w h y

Answered by nume1114 last updated on 15/Dec/16

i) I f i > 0

i \cdot i > 0 \cdot i

- 1 > 0 \dots [c o n t r a d i c t i o n]

ii) I f i < 0

i \cdot i > 0 \cdot i

(m u l t i p l y b o t h s i d e s b y - v e n u m b e r s)

- 1 > 0 \dots [c o n t r a d i c t i o n]

f r o m i) a n d ii), i ≯ 0 a n d i ≮ 0 .

Commented by geovane10math last updated on 15/Dec/16

t h a n k s

Answered by FilupSmith last updated on 15/Dec/16

i \in C, 0 \in R

R \subseteq C \Rightarrow C ⊈ R

∴ i ⪇ 0 \land i ⪈ 0

∵ i \notin R