a real number proof question..

[transgalactic]

i got a real number called "x"

prove that if it follows this rule n>x>=0

for every real and positive "n"

then "x" must have the value x=0

??

i dont know how to solve it because
from this expression
n>x>=0

"x" must not be equaled to 0

i cant see the way to solve it

??

 

[victoriamath]

Suppose x > 0 say x = a > 0. Now choose n < a.

 

[transgalactic]

if you say that a=x>0 and a>n then it gives us a conclusion that x>n

then its contradicting the demands of the question
n>x>=0


??

 

[transgalactic]

real number proof..

prove that if x is a real number which satisfies n>x=>0 for every positive n
then x must have the value x=0


x can have the value 0

but it doesnt has to equaled to 0

??

 

[daon]

Re: real number proof..

What do we know thus far?

As far as I know "positive integer" means "greater than or equal to 1."

 

[transgalactic]

Re: real number proof..

it doesnt prove that X must ne equaled to 0
??

 

[transgalactic]

Re: real number proof..

They´re telling me that a positive real number x is smaller than ANY positive real number n. So n "pushes" x to the 0.

how to say that in math?

 

[daon]

Re: real number proof..

I assumed n was an integer, as it usually stands for one, and you did not quantify it. In that case, no, n does NOT push x to zero. x=1/2 is a perfectly good counter example.

If n stands for a REAL then yes. Assume x>0. Then letting n=x/2 manufactures a contradiction.