Which sounds better: (they say the same thing)
All the toothpastes were found to have the same effectiveness.
No toothpaste has been found more effective than "Crust".
Consider the following values:
5 5 5 5 5. We can say the following.
All numbers are equal to 5. All x are equal to y.
No number is greater than 5. No x is greater than y.
No number is less than 5. No x is less than y.
All numbers are less than or equal to 5. All y are less than or equal to x.
All numbers are greater or equal to 5. All x are greater than or equal to y.
A common self-deception is to
not realize that all the values are at the same level.
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.
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]
13:32 Which indeed is the least of all seeds: but when it is grown, it is the greatest among herbs, and becometh a tree, so that the birds of the air come and lodge in the branches thereof. [kjv]
