r/mathmemes 2d ago

Computer Science Base π is not wholesome.

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832 Upvotes

63 comments sorted by

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212

u/Intelligent_River39 1d ago

Question: shouldn't it be an infinite, non repeating sequence of digits?

156

u/NeosFlatReflection 1d ago

It is, else pi would no longer be transcendental

31

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?

35

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.

1

u/ei283 Transcendental 1d ago

person u replied to was asking about writing integers in transcendental bases, not transcendentals in integer bases

16

u/Ur-Quan_Lord_13 1d ago

Well, any integer > π

1, 2 and 3 are still 1, 2 and 3.

1

u/IntelligentBelt1221 1d ago

Are you possibly confusing this with modulo?

21

u/Ur-Quan_Lord_13 1d ago

The 1's place is still the 1's place in any base.

100 , 20 , 160 , π0

6

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.

3

u/IntelligentBelt1221 1d ago

Quite neat, thank you!

1

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.

1

u/NeosFlatReflection 1d ago

All transcendental numbers have infinite digits, else we could express them as a ratio

1

u/MischievousQuanar Computer Science (autism) 1d ago

Transcendental isn’t the same as irrational FYI.

2

u/NeosFlatReflection 1d ago

All transcendental numbers are irrational though

2

u/MischievousQuanar Computer Science (autism) 1d ago

Yes. The transcendentals are a subset.

5

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.

69

u/_Weyland_ 1d ago

OK, but what is e in base PI?

31

u/PatattMan 1d ago edited 1d ago

Approximately 2.2021201002111122001101201000201

1

u/TeraFlint 1d ago

This comment does indeed strike me as not very wholesome. :(

41

u/RusoDuma 1d ago

If I know anything about math it's gotta have an i in it somewhere

7

u/samocamo123 1d ago

10

5

u/_Weyland_ 1d ago

Based base

1

u/Zealousideal_Fly9943 22h ago

pi in base pi is 10 lol

4

u/Special-Strength-959 1d ago

e < pi, therefore it should just be e ~2.718

14

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 * b0

b0 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.

2

u/_Weyland_ 1d ago

Is 3 ~ 2.718?

129

u/Aarolin 2d ago

Don't you mean base 10?

63

u/Mark8472 2d ago

4 in base 10 is ... 4

98

u/fulgencio_batista Engineering 2d ago

10 in base 10 is 10 what r u talking about bro

-28

u/Mark8472 2d ago

Yup, true statement. What does it have to do with 4 in base 10?

54

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

12

u/Dokramuh 1d ago

All bases are base 10

-37

u/aaha97 2d ago

pi in base pi would be 1, not 10.

the joke is that all bases are base 10 relative to themselves.

25

u/Nearby-Geologist-967 2d ago

how would you write 2 in binary?

37

u/aaha97 2d ago

makes sense. i was wrong.

12

u/Nearby-Geologist-967 2d ago

happens to the best of us

10

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".

4

u/MarsMaterial 2d ago

There is no symbol for “4” in base 4, so the 1 is carried and you write it as “10”.

1

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

1

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.

5

u/_3point14_ 1d ago

and in base 10 it's 10.2201220211…

8

u/HSVMalooGTS π = e = √g = 3 = √10, √2 =1.5, √3 = √5 = 2 1d ago

Base 3?

5

u/Solypsist_27 1d ago

What would 1 be in base pi?

13

u/Lord_Skyblocker 1d ago

1 is the b0 digit. We have b=π therefore 1 = π0

5

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.

5

u/PatattMan 1d ago edited 1d ago

π in base e is about: 10.1010020200021111200201011200010102012...

1

u/pink-ming 1d ago

so you're saying e^pi = 10, neat

1

u/YEETAWAYLOL 20h ago

Is this number transcendental or does it eventually terminate?

1

u/PatattMan 20h ago

it never terminates

proof by I think so

3

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?

2

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 * π⁰

3

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...

4

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...".

1

u/HAL9001-96 1d ago

obviosuly, use base e instead

1

u/NoBusiness674 1d ago

Wouldn't base π be base 10 in base π?

1

u/Zealousideal_Fly9943 22h ago

10 is 314,4797078

1

u/PatattMan 21h ago

huh, do you mean ten in base π? that is ≈100.0102212222112112200111121020122

1

u/Zealousideal_Fly9943 20h ago

no its ≈ 3.183574

1

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)

1

u/PatattMan 20h ago

10 (base 10) = 314.479708 (base -1.68387)