Proving F is not an increasing function?

[mdlavey]

1. (Initial Question) let f be a function from R to R. Without using words of negation, write the meaning of "f is not an increasing function."



2. No Relevant Equations.



3.(Attempt at Solution) Does this mean that I just need to rewrite the statement without using the word "not", or am I somehow supposed to prove that f is not an increasing function? If I am supposed to prove this, how would I go about that?

Thanks!

 

[LCKurtz]

1. (Initial Question) let f be a function from R to R. Without using words of negation, write the meaning of "f is not an increasing function."



2. No Relevant Equations.



3.(Attempt at Solution) Does this mean that I just need to rewrite the statement without using the word "not", or am I somehow supposed to prove that f is not an increasing function? If I am supposed to prove this, how would I go about that?

Thanks!

Neither. You just need to fill in the blank spot in this:

If f is a function from R to R such that ____________________________, then f is not an increasing function on R.

You have a definition of increasing function to use to help you fill in the blank.

 

[HallsofIvy]

There exist some x and y such that x< y but ... What will be true of f(x) and f(y) to show that f is NOT increasing?