This is a Journal entry by Andyman

Irrational numbers.

Post 1

Andyman

Somehow, as an offshoot to a conversation about the existence of God, I ended up trying to explain why I "don't believe in irrational numbers." I'd like to use this journal entry to flesh out some of my ideas.

And bear in mind, this is only recreational theoretical mathematics. I'm not a mathematician.

I placed "don't believe in irrational numbers" in quotes above because that is the simple way to put it. What I actually believe is that irrational numbers do not correspond to anything in the real universe. Why do we have numbers/numerals in the first place? At first they were just for counting things. Someone needed a shorthand way to keep track of how many cows they had. Eventually, the hash marks got to be too inconvenient, so someone created one symbol that represented a larger number of hash marks. And, voila, numerals are born.

Later, people wanted to be able to measure other things that couldn't be simply counted, probably mostly for comparison's sake. Perhaps a greedy king wanted to make sure that he owned more land than all of the other lords combined. Perhaps an giving king wanted to equally divide his land among his 17 lords. Axiom by axiom, mathematics was born. Necessity once again is the mother of invention.

So where did irrational numbers come from?

Irrational numbers, of course, are infinitely long non-repeating decimals. Pi is an irrational number. Any rational number times any irrational number equals an irrational number. You can't multiply two irrational numbers because, frankly, you need to be able to figure out (much less see) what each of the numerals in a number is before you can really multiply. At any rate, if you could multiply two irrational numbers, you would probably get another irrational number.

So, if we accept that pi times the diameter of a circle gives us the circumference of that circle, then it is impossible for a circle to have both the diameter and the circumference be rational numbers. That seems like a bunch of malarkey to me.

Please dont' respond to this yet. I have more to say. . .smiley - run


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Irrational numbers.

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