Oh my; are you the rebellious one?
Doesn't everybody rebel a little? Especially when someone is being so doggone particular?
I do declare it's been a coon's age since I last saw ya; juhere that former Dallas Cowboys' coach Jimmy Johnson recently toured the University of Alabama?
That depends; inequalities are governed by the following properties. Note that, for the transitivity, reversal, addition and subtraction, and multiplication and division properties, the property also holds if strict inequality signs (<and>) are replaced with their corresponding non-strict inequality sign.
The trichotomy property states:
For any real numbers, a and b, exactly one of the following is true:
a <b> b
The transitivity of inequalities states:
For any real numbers, a, b, c:
If a > b and b > c; then a > c
If a < b and b < c; then a <c> b then b < a
If a <b> a
The properties which deal with addition and subtraction state:
For any real numbers, a, b, c:
If a > b, then a + c > b + c and a − c > b − c
If a < b, then a + c < b + c and a − c < b − c
i.e., the real numbers are an ordered group.
The properties which deal with multiplication and division state:
For any real numbers, a, b, c:
If c is positive and a < b, then ac < bc
If c is negative and a <b> bc
More generally this applies for an ordered field, see below.
The properties for the additive inverse state:
For any real numbers a and b
If a <b> -b
If a > b then -a < -b
The properties for the multiplicative inverse state:
For any real numbers a and b that are both positive or both negative
If a <b> 1/b
If a > b then 1/a < 1/b
If we consider two cases of functions: monotonic and strictly monotonic.
Any strictly monotonically increasing function may be applied to both sides of an inequality and it will still hold. Applying a strictly monotonically decreasing function to both sides of an inequality means the opposite inequality now holds. The rules for additive and multiplicative inverses are both examples of applying a monotonically decreasing function; in which case: Less = More!
So, do you now care more or less?
Does that really apply to the caring quotient of the female brain, though?
I am sorry I am unable to answer that question; can you find it in your heart to forgive me?
Do you really need to be forgiven?
Don't we all at some point?
Some more than others don't you think?
:wink: (me!)
Do you know; I forgive you?
You know how to make a girl feel happy don't you?
...by the way, what did I do?
Is innocence a valid defense?
Is innocence a defense or a verdict?
Are you trying to confuse me?
How could I confuse an intelligent, well-grounded man like yourself?
How about you line up three hammers and ask me to take my pick?
what? Who's confused now?
What would Confucius say?
who the hell's Confucius? :wink:
