What is the difference between an increasing and decreasing function?

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- Jan 19th 2007, 07:51 PMsymmetryIncreasing & Decreasing Functions
What is the difference between an increasing and decreasing function?

- Jan 20th 2007, 12:22 AMCaptainBlack
1. A function f(x) on the real line is increasing if:

for all x, y in R, such that if x>y, then f(x)>=f(y).

2. A function f(x) on the real line is strictly increasing if:

for all x, y in R, such that if x>y, then f(x)>f(y).

3. A function f(x) on the real line is decreasing if:

for all x, y in R, such that if x>y, then f(x)<=f(y).

3. A function f(x) on the real line is strictly decreasing if:

for all x, y in R, such that if x>y, then f(x)<f(y).

1a. A function f(x) on an interval I of the real line is increasing if:

for all x, y in I, such that if x>y, then f(x)>=f(y).

2a. A function f(x) on an interval I of the real line is strictly increasing if:

for all x, y in I, such that if x>y, then f(x)>f(y).

3a. A function f(x) on an interval I of the real line is decreasing if:

for all x, y in I, such that if x>y, then f(x)<=f(y).

3a. A function f(x) on an interval of the real line is strictly decreasing if:

for all x, y in I, such that if x>y, then f(x)<f(y).

RonL - Jan 20th 2007, 06:32 AMsymmetryR
I understood your words.

However, what does the upper case R mean? - Jan 20th 2007, 08:26 AMCaptainBlack