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Originally Posted by protagonist
But 1/3 is irrational, not 0.333333333.
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Let me introduce you to φ.
φ is a nifty number. It is approximately 1.61803, but not exactly. You could try to express it as the ratio between two integral numbers, but you will inevitably fail, and not because you suck at numbers. 16:10 is a pretty good approximation, but not the exact thing, because φ is slightly more than that. 16:9 or 17:10 are not exactly better.
So, you can apply some fancy math on φ's definition which I will skip and you get φ = (1+sqrt(5))/2. This is so complicated because φ is not just any number like 4, 15.3 or 343209443214, but inherently
irrational.
Now, compare φ to 1/3. As you might notice, most of what I said about φ does not apply to 1/3. 1/3 is exactly 1/3 and not some crazy fraction with square roots and other mathematical gadgets. You can easily say 1/3 using the two integral numbers 1 and 3. Even without fancy math. I think that makes 1/3
rational.
So please stop responding to my posts.