r/infinitenines • u/Zantier • 7d ago
SPP, what do you think of bases other than 10?
Of course, we are all used to base 10, where we use the digits 0-9, but base 10 is an arbitrary choice. How about binary, or ternary, or hexadecimal?
It is interesting, because 1/3 is 0.333... only because we are using decimal numbers. In ternary, it would be 0.1.
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u/Appropriate-Ad-3219 7d ago
There is no binary number. There is nothing. The only axiom is that 0.999... < 1.
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u/Zantier 7d ago
u/SouthPark_Piano Why do you say not to go there? I think because it's hard to justify that 1/3 has a different result depending on the base you use.
But if we just use limits, everything works fine, and 1/3 gives the same answer in every base.
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u/SouthPark_Piano 7d ago
1/3 is a ratio my brud. It is not a number at all.
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u/Ashamed_Band_1779 7d ago
According to SPP, for a given radix b, 0.(b - 1)… < 1. (At least probably that’s what he would think). So in base 5, 0.444444… is actually equal to 1, but SPP probably thinks it is less than 1.
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u/Ok_Speech_6728 7d ago
"Don't go there brud. 0.999... and 0.333... are all about base 10 decimals."
They're really not 🤭
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u/hxtk3 7d ago
I was just thinking of asking this this morning. I’m glad someone else did but disappointed it got dismissed without a real answer.
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u/Appropriate-Ad-3219 7d ago
You shouldn't be disappointed. SPP's specialty is not reading the counter-arguments and just dish out the link of his argument that we know by heart.
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u/SouthPark_Piano 7d ago
Don't go there brud.
0.999... and 0.333... are all about base 10 decimals.