If f(x) is a continuous function for a

Question

If f(x) is a continuous function for a<or= x <or= B, this interval is divided into n equal subdivisions and the width of each subdivision is delta t, so delta t = (b-a)/n...first of all, can delta t ever be negative? Under what circumstances? And can the subdivisions be unequal?

ranga · Answer

delta_t = (b - a) / n
since a <=  x  <= b,   (b-a) >= 0.  And n is positive.  So delta_t is positive.

anonymous · Answer

but can delta t ever be negative? Is it possible for delta t to be negative in a continuous function?

ranga · Answer

I don't think so because we take an interval and divide it into n equal parts.  
An interval always has a certain positive width which when divided by positive n will always yield a positive width for each sub-interval.

ranga · Answer

Whether the interval is on the positive x axis, negative x-axis, or crosses from negative to positive,  the width of the interval is the rightmost point - leftmost point which will always be positive.  When divided into n equal parts the sub-interval (or delta_t) will always be positive.

anonymous · Answer

oh, I see. Thanks again!