Question

what is a counter example of x>1/x

Answer 1

is it\[x<\frac{ 1 }{ x } ?\]

Answer 2

thank you , I have tru=ouble figuring out counter examples to prove a statement is false

Answer 3

I need to prove that this equation is not always correct

Answer 4

mathematical Excursions

Answer 5

\(\Huge\color{blue}{ \sf x< \frac{1}{x} }\)

\(\Huge\color{blue}{ \sf 2< \frac{1}{2} }\)
well, 1/2 is less than 2, not greater than 2.


\(\Huge\color{green}{ \sf x> \frac{1}{x} }\)

\(\Huge\color{green}{ \sf .5> \frac{1}{.5} }\) ... \(\Huge\color{green}{ \sf 1/2> 2 }\)

Answer 6

When you explain it like that it makes sense. Thank you Solomon

Answer 7

You welcome :)

Answer 8

i did not follow your question.
let x>0
\[x>\frac{ 1 }{ x },x^2>1\]
\[\left| x \right|>1,x<-1(rejected) ~and~x>1\]
it is false in 0<x<1

Answer 9

let x<0
\[x>\frac{ 1 }{ x },x^2<1,\left| x \right|<1,-1<x<1\]
it is true in -1<x<0
for all other negative values it is false.

Answer 10

Thank you for the help

Answer 11

yw