Is This Function Increasing for Any or Some x?

[holezch]

Hi, I need help with this definition. It seems pretty vague to me:

A function f is increasingat a if there is some number delta > 0 such that

f( x ) > f ( a ) if a < x < a + (delta)

and

f( x ) < f( a ) if a - (delta) < x < a


My problem is that 'x' was never quantified... is this for ANY x that satisfies a < x < a + (delta), or some x that satisfies a < x < a + (delta) ?

thanks...

 

[Martin Rattigan]

Any x.

 

[holezch]

thanks, I've got it