The correspondence between relational operators can be confusing to some.
The purpose of
algebra is to work through problems
without having to think about what it means. It is just
symbol manipulation. Much of computer programming is
algebra and
symbol manipulation and
not thinking like a computer.
Do you remember the commercial for toothpaste, here called "
Crust"? It went something like the following.
Extensive research studies by independent researchers found that no toothpaste has been found to be more effective than "
Crust" in doing good things for your teeth.
So the "
Crust" toothpaste must be pretty good. Is that correct?
It turns out that, in this (hypothetical) study, all toothpastes studied had the same results (within experimental error). Thus there was no best and no worst one.
Marketing words to the rescue.
No toothpaste has been found more effective than "
Crust"!
Most people will not recognize the fine distinction.
Suppose we have the following numbers.
5 5 5 5 5
We can say the following.
No number is greater than 5.
All numbers are greater or equal to 5.
All numbers are equal to 5.
No number is less than or equal to 5.
No number is less than 5.
We can also say the following, where
x, is one of the numbers.
No other number is greater than x. (marketing use if high score is best, as in "No other number was found to be more effective than our brand.")
All numbers are greater or equal to x.
All numbers are equal to x.
No number is less than or equal to x.
No other number is less than x. (marketing use if low score is best)
A common self-deception is to not realize that all the values are at the same level.
Matthew 13:31 Another parable put he forth unto them, saying, The kingdom of heaven is like to a grain of mustard seed, which a man took, and sowed in his field: [kjv]
