montrer-que-le-quotient-d-un-nombe-rationnel-et-dun-nombre-irrationnel-est-irrationnel-

Question Number 159994 by mathocean1 last updated on 23/Nov/21

montrer que le quotient d^{'} un

nombe rationnel et dun nombre

irr a tionnel est irrationnel

Answered by Tokugami last updated on 23/Nov/21

show that the quotient of a

rational number and an irrational

number is irrational .

proof by contradiction :

\frac{r_{1}}{i_{1}} = r_{2} \begin{matrix} r_{1}, r_{2} \in Q & i_{1} \in R - Q \end{matrix} \underset{⏟}{}

\frac{r_{1}}{r_{2}} = i_{1}

\frac{a / b}{c / d} = i_{1} a, b, c, d \in Z

\frac{a c}{b d} = i_{1}

this would mean that a ratio of integers is irrational

the opposite must be true .

Commented by mathocean1 last updated on 23/Nov/21

p l e a s e c a n y o u d e t a i l s i r