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Rational, Irrational, and Integer. The correct definition.
Peter Taylor:
This is the new and correct definition of a number.
1/ A number must be an integer.
2/ The term rational and irrational don't apply to a number by definition 1/.
An integer is any number that can be defined wholly. For instance, 7, and 1 / 7 can be defined wholly and are therefor integers.
An equation that cannot be defined wholly, such as root 2, where we don't know what number multiplied by itself equals 2, remains a question, and is not a number by definition 1/.
A number can't be rational or irrational. These terms have no meaning.
Thankyou. :D
TimFox:
No.
gnuarm:
Why are you making up your own math? I'm not following what you are trying to do.
SiliconWizard:
Is this a philosophical issue you have with non-integer numbers (and well, why not, although that's a bit odd, but a deep philosophical approach about this could be interesting, maybe), or is it because you have a problem fully understanding them?
If that's the former, you may want to elaborate (although it's not guaranteed to get much traction.) Otherwise that's just your own definition with nothing to back it up except itself, which, you'll have to admit, is a bit circular.
gnuarm:
I know there are different levels of infinity. There are an infinite number of integer numbers. You can pick two integers so there are not integers between them. Then, between these two integers, there are an infinite number of rational numbers.
Here's where it gets tricky. There are an infinite number of irrational numbers between any two rational numbers. But can you select a pair of rational numbers, that have no other irrational numbers between them?
Clearly, integers and rational numbers are different sizes of infinity. But I'm not sure that is true for rational and irrational numbers.
Don't even get me started about transcendental numbers.
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