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Rational, Irrational, and Integer. The correct definition.
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TimFox:

--- Quote from: magic on December 21, 2022, 10:12:18 am ---
--- Quote from: SiliconWizard on December 21, 2022, 04:01:29 am ---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?

--- End quote ---
Hardly anyone who hasn't done at least a BS in maths understands what the irrationals are so it's the latter obviously :P

And yeah, Deja vu ::)

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I learned about irrational numbers in high-school mathematics at a US public school.
eugene:

--- Quote from: Peter Taylor on December 21, 2022, 03:43:02 am ---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

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I doubt anyone would object to you inventing your own, private version of math. I also doubt that very few people would be interested, but I'm pretty sure nobody would object.

What lots of people object to is redefining terms that are already well defined in the old (and still correct) math. So, my advice, if you hope to get any reaction other than negative, is to stay away from existing terms like "integer", "rational", and "irrational" and coin your own NEW terms to go along with your NEW math. You don't always need to tear down something old to build something new.
magic:

--- Quote from: TimFox on December 21, 2022, 04:39:44 pm ---I learned about irrational numbers in high-school mathematics at a US public school.

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Cool.

So I gather that the naturals are an extension of counting fingers beyond the actual number of fingers you might have, the integers are the naturals mirrored around zero, the rationals are fractions of the integers, and complex numbers are what happens when you imagine that sqrt(-1) is a thing.

So what the hell are the irrationals, then?
Something about continuous divisions and stuff?
But you have heard about those "atoms" and "quantum" stuff, right?
There is nothing real about real numbers.

The theory that they are an inside joke of heterosexual European men invented to confuse Americans doesn't even seem so far off :P
TimFox:
"rationals" are ratios of integers
"irrationals" are not ratios of integers
magic:

--- Quote from: TimFox on December 21, 2022, 06:08:34 pm ---"irrationals" are not ratios of integers

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This definition is not a ratio of integers either ;)
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