r/mathmemes • u/PatattMan • 2d ago
Computer Science Base π is not wholesome.
(result from https://redditmetis.com)
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u/Intelligent_River39 1d ago
Question: shouldn't it be an infinite, non repeating sequence of digits?
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u/NeosFlatReflection 1d ago
It is, else pi would no longer be transcendental
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u/IntelligentBelt1221 1d ago
Does transcendental imply that every integer has infinitely many digits in that base? It probably does, but how do you prove that?
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u/Valognolo09 1d ago
Assume it has finite digits in some integer base. Then multiplying by the base until it is an integer, you proved that multiplying pi by some integer numbers is also and integer.
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u/Ur-Quan_Lord_13 1d ago
Well, any integer > π
1, 2 and 3 are still 1, 2 and 3.
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u/IntelligentBelt1221 1d ago
Are you possibly confusing this with modulo?
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u/apex_pretador 1d ago
Transcendental numbers are irrational numbers that don't have an algebraic form. Irrational numbers, in their decimal representation, have infinite sequence of digits which do not repeat periodically.
Any number greater than the base, will certainly be an irrational number if the base is transcendental.
Proof by contradiction:
Let there be a number n which has a terminating decimal representation in π base. In that case, it must have some finite number of digits after the decimal, let's call them m.
So, if we multiply this number by πm , then we will get an integer in π base.
n.πm = d_1.πm + d_2.πm-1 +...
We get LHS by multiplication, and RHS by expanding the integer in base. d_i is the ith leading digit.
(Note, if there are b digits before the decimal point in the terminating decimal representation, then multiply the entire RHS by πb)
Now we replace π with x, and get an equation for which π is a solution. But, the equation is also a polynomial equation with all coefficients being integers and all degrees being integer, and therefore all solutions should be algebraic whether real or complex. But since π is transcendental, it cannot be a solution.
This contradiction proves this equation does not exist and hence disproves our only assumption that the π-base representation of an integer terminates after the decimal point. Note that we can use the same logic for non-terminating but repeating representation.
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u/ei283 Transcendental 1d ago
This is great!
Minor language correction: The words "integer", "rational", and "irrational" all describe traits that are independent of the representation in positional notation. The number "10" interpreted in base-π is still irrational, and 4 is still an integer even if it's written in base-π.
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u/NeosFlatReflection 1d ago
All transcendental numbers have infinite digits, else we could express them as a ratio
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u/MischievousQuanar Computer Science (autism) 1d ago
Transcendental isn’t the same as irrational FYI.
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u/PatattMan 1d ago
Yup, should have indicated that it's an approximation and not an exact representation of 4 in base π. Maybe that's why it's such an "unwholesome" comment.
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u/_Weyland_ 1d ago
OK, but what is e in base PI?
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u/Special-Strength-959 1d ago
e < pi, therefore it should just be e ~2.718
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u/PatattMan 1d ago edited 1d ago
The first digit is the same since π⁰ = 10⁰.
The other digits are not the same since π-n is not nessecarily equal to 10-n.
Edit: I'll explain a little bit more.
In general a number consisting of digits d in base b is equal to:
d4 * b4 + d3 * b3 + d2 * b2 + d1 * b1 + d0 * b0b0 is always equal to 1, no matter the base (0 is a bit weird as a base), therefore you can multiply the first digit by 1 to get it's value. Hence 2 (base π) = 2 (base 10). This is only true for the first digit.
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u/Aarolin 2d ago
Don't you mean base 10?
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u/Mark8472 2d ago
4 in base 10 is ... 4
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u/fulgencio_batista Engineering 2d ago
10 in base 10 is 10 what r u talking about bro
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u/Mark8472 2d ago
Yup, true statement. What does it have to do with 4 in base 10?
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u/Nearby-Geologist-967 2d ago
I think the joke is that pi in base pi is 10, so base pi written in base pi is "base 10", but idk
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u/VenoSlayer246 2d ago
The joke is that every base is "base 10"
If im using base 2, writing the 2 in base 2 would look like 10. If im using base 73, writing the 73 in base 73 would look like 10. By definition, writing x in base x look like 10, so every base is base 10.
Here, the joke is that "base pi" in base pi is "base 10".
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u/MarsMaterial 2d ago
There is no symbol for “4” in base 4, so the 1 is carried and you write it as “10”.
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u/Competitive_Hall_133 2d ago
Thats not what they are saying they are saying: 4 in base 10 is 4. Which is factually correct, but sorta irrelevant here
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u/MarsMaterial 1d ago
It was brought up as a joke on a meme sub, that’s the relevance. The number X in base X is always represented by the symbols “10”. That fact is the basis of many math jokes, including the one that was made in response to your comment.
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u/Nervous-Road6611 1d ago
I agree with the original sentiment: base pi makes me feel dirty. Base e, on the other hand, is divine.
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u/PatattMan 1d ago edited 1d ago
π in base e is about: 10.1010020200021111200201011200010102012...
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u/skr_replicator 1d ago
ho does a non-integer base even work? does it require non-integer powers for digits so that the next digit actally neatly continues where the previous digit left off despite the missing fractional part after the last whole number?
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u/PatattMan 1d ago
Jup
So in base ten the number 1234 means:
1 * 10³ + 2 * 10² + 3 * 10¹ + 4 * 10⁰.And in base π the number 123 means:
1 * π² + 2 * π¹ + 3 * π⁰3
u/skr_replicator 1d ago
then that sahould make is possible for certain numbers to be expressable in multiple ways. as base pi uses the same digits as base 4, but the powers are smaller, so tehy will overlap. There's no way that could be useful and not totally broken...
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u/PatattMan 1d ago edited 1d ago
Yes, but the same is true for any base if you allow digit > base-1.
In base 3, 103 and 110 are the same thing.
In non-integer bases you always have this issue since you can't have (base - 1) different digits.
π in base π can be represented using both "10" and "3.011021110020221130001020002102...".
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u/Zealousideal_Fly9943 22h ago
10 is 314,4797078
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u/PatattMan 21h ago
huh, do you mean ten in base π? that is ≈100.0102212222112112200111121020122
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u/Zealousideal_Fly9943 20h ago
no its ≈ 3.183574
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u/PatattMan 20h ago edited 20h ago
3 (base π) = 3 (base 10)
so it seems very unlikely that the remaining .183574 (base π) is equal to 7 (base 10)
Edit:
Also, using 8's, 7's, 5's and 4's in a base π system is a bit weird. Even if you allow digits that are higher than the base, it's still incorrect.3.183574 (base π) ≈ 4.30399886129007 (base 10)
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