Prove that this statement holds true for ALL REALS

G

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Statement: For all real numbers x, if x > 1, then 1/x < 1

I have tried it and substituted values for x
Is this how u prove this?

Thank you in advance.
 
Nope, no matter how many numbers you find that do work, that doesn't prove there isn't one number that doesn't work.
Can't you just divide both sides of the premise by x (since we know it isn't < 1) to get
x > 1
1 > 1/x so
1/x < 1
 
Note that the proof in the previous post depends on x being greater than 1, so that x is, in particular, greater than zero. This is what allows you to divide through by x. (Otherwise, that step would be illegitimate, since otherwise the sign of x would be unknown.)

Eliz.
 
thank you for both of your answers...

I was thinking of using proof by mathematical induction?
 
americo74 said:
I was thinking of using proof by mathematical induction?
Click to expand...
Since the proof is supposed to cover all real numbers, not just the naturals, I don't see how induction would work.

What is your objection to the proof already provided?

Please include specifics. Thank you.

Eliz.
 
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