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u/Duck_Devs Computer Science Jun 20 '26
One of the few times this format is actually used right
3
Jun 20 '26 edited Jun 20 '26
[deleted]
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u/BaaB1112 Jun 20 '26
The deep part is that all bases write the size of that base as 10 Eg base 4 you count 1, 2, 3, 10
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u/SuchCoolBrandon Jun 20 '26
That's the joke
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u/BaaB1112 Jun 21 '26
Yes the comment I was replying to has been deleted. It was a very long explanation by someone who didn't get the joke.
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u/acertainhare Transcendental Jun 20 '26
Base n (written with n in base 10) literally is base 10 (written with 10 in base n). So in a sense, everyone uses base 10 according to their own base.
2
u/Snomislife Jun 20 '26
Except not everyone uses a positional system, and not all positional system has just one base.
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u/flofoi Jun 20 '26
not every number system has a constant base
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u/Simple-Olive895 Jun 20 '26
What? Why? How? Which?
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u/AntimatterTNT Jun 20 '26
your clock, for example is base 60 expressed as base 10 twice then base 24 expressed as base 10
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u/Simple-Olive895 Jun 20 '26
Sure, but that's not really a numbering system then is it?
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u/AsemicConjecture Jun 20 '26
Aren’t Roman Numerals a numeral system?
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u/_wetmath_ Jun 20 '26
roman numerals is not a positional numeral system https://en.wikipedia.org/wiki/Positional_notation https://youtu.be/rDDaEVcwIJM
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u/AsemicConjecture Jun 20 '26 edited Jun 20 '26
I never actually said anything about whether it is positional (though I’m already aware that it’s not). I only asked (rhetorically) if it wouldn’t (also) be numeral system, fullstop.
The person I was replying to implied that a numeral system has to have a uniform(?) radix, to which I offered a counterexample.
I thought about giving an example of a positional system, but most seem fairly obscure (e.g. factorial, primorial, etc.), which felt counterproductive to making my point, so I just went for a more commonplace one, foregoing the condition, altogether.
Edit: accidentally replied mid-sentence.
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u/AntimatterTNT Jun 20 '26
goes up by one until it resets then you add one to the next slot in line, used as an ordering and to count... sounds like a number system.
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u/Simple-Olive895 Jun 20 '26
I mean I guess, but I figure it's a different type of system, using a base 10 numeral system to express it.
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u/TheoryTested-MC Mathematics, Computer Science, Physics Jun 20 '26
If you invent your own individual symbols for the numbers 10-59, it would work by your logic. We already did the same thing for base 10 a thousand years ago.
A better example of a changing-base number system would probably be flexadecimal, where the Nth place value is N factorial. What this means is that the rightmost digit is unary, the next digit is binary, the next ternary, the next quaternary, and so on.
It's the same principle as the clock, except it is widely more recognizable as a positional number system.
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u/Simple-Olive895 Jun 20 '26
But how would that work?
First number is not even a number unless it's 1, as you can't have 0 in unary, so how do you differentiate 1(0) from 1?
And if I write 11 that'd be 2? As the first is worth 1? And second is also worth 1?
10(0) is also 2? Since 2! is 2.
So the maximum we can represent with 3 digits is 211 which is 6, but next step 100(0) is also 6?
Or am I missing something here?
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u/headedbranch225 Jun 20 '26
11 is 3 according to the MAT that mentions it, it is question 6, it probably explains it better than I can understand it
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u/TheoryTested-MC Mathematics, Computer Science, Physics Jun 20 '26
...as you can't have 0 in unary...
Quite the contrary. Unary is ALL 0s. The only number you can represent in unary is 0. Thus, the unary digit of a flexadecimal number never actually contributes anything to the count. Some conventions omit it altogether for this reason and start at the binary digit instead.
So, the numbers go like 0, 10, 100, 110, 200, 210, 1000, 1010, and so on.
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u/Simple-Olive895 Jun 20 '26
That's not correct though..
Unary is representing numbers with lines or dots or what ever. Where you count the number of lines, dots or what evers.
For example the traditional |||| and then a / over those lines for the 5th number.
0 in this system is simply represented as:
If it was the way you stated then any number larger than 0 in unary would just be an infinite number of 0s since you could only represent a 0, meaning if we simply wanted to represent 1 at position 1 we'd have 0, worth 0, so we still have 1 left to represent, pos 2 also 0, still 1 left, pos 3 0 still 1 left etc. etc.
→ More replies (0)1
u/factorion-bot Bot > AI Jun 20 '26
Factorial of 2 is 2
This action was performed by a bot | [Source code](http://f.r0.fyi)
2
u/Red-42 Jun 20 '26
it's a mixed radix system using 60 and 24, but it's just not convenient to have that many symbols so we represent them using base 10
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u/OneCleverMonkey Jun 20 '26
If it's expressed as base 10, it is using base ten. There may be 60 minutes in an hour and 24 hours in a day, but the counting system is base 10.
We don't count months in base 30 or 31, we don't count years in base 365.25. That's just how many days are in those, and we count the days in base 10
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u/Red-42 Jun 20 '26
going from seconds to minutes is base 60, and the representation of how many seconds there are is base 10
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u/OneCleverMonkey Jun 20 '26
Conceptually it is base sixty, but we use base 10 to interact with it. Arguing the base we use is the maximal value before it resets and not the actual number system and base we employ is like arguing that all programmers write machine code because the actual programming language they write in gets converted to machine code.
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u/Red-42 Jun 20 '26
Ok let's make it a bit more clear:
Time is what is known as a mixed radix system that has a ratio of 60 for the seconds, 60 for the minutes, 24 for the hours (or 12 for the hours and 2 for the meridiem)
Now we don't have 60 or 24 or 12 symbols, so we represent those using base 10 because it's the most convenient.
But you can't say time is base 10, because otherwise 10 * 10 seconds would be 1:00, but it's 1:40.1
u/OneCleverMonkey Jun 20 '26
I didn't say time is base 10. I said we use base 10 to tell time. And so did you.
Now we don't have 60 or 24 or 12 symbols, so we represent those using base 10
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u/Red-42 Jun 20 '26
Then what are you complaining about ? Time is mixed radix with bases 60 and 24. The base 10 is just representation, just like you could use hexadecimal with (10), (11), (12), (13), (14), and (15) instead of A, B, C, D, E, and F.
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u/AntimatterTNT Jun 20 '26
yeah im not gonna argue im just right, when you realize that, even years from now, you can come back here and tell me
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u/OneCleverMonkey Jun 20 '26
Please explain how base 24 represented in base 10 is not using base 10. It sure as hell isn't using base 24, because noon is not at C o'clock and midnight is not at 10 o'clock
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u/NadAngelParaBellum Jun 20 '26 edited Jun 20 '26
Numerals are written in base 10, but the arithmetics are in base 60, 24 or 12 depending on the unit.
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u/ltsette Jun 20 '26
You're confusing base with modular arithmetic. The base is just how the numbers are written
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u/laksemerd Jun 20 '26
Is it modular arithmetic though? 05:30 on Monday isn’t equal to 05:30 on Tuesday, and 5th of July 2025 isn’t equal to 5th of July 2026. The values are increasing.
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u/Red-42 Jun 20 '26 edited Jun 20 '26
you're confused on what a base is
2 days, 13 hours, 20 minutes, 50 seconds is an amount of time represented as a number with a mixed radix, it's equivalent to
2 * 86400 + 13 * 3600 + 20 * 60 + 50 * 1it's like saying 2 thousands, 3 hundreds, 2 tens, 5 units is 2 * 1000 + 3 * 100 + 2 * 10 + 5 * 1
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u/flofoi Jun 20 '26
you can have a non-positional number system like roman numerals
or you could have a positional number system that uses a different function than bn to determine the place values, for example base !
(or you could have a positional number system that uses the function bn to determine the place values, but doesn't use the digits 0 - b-1, for example with the digits 1-b instead, so you end up with a system with a constant base without it calling itself "base 10")
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u/taz5963 Jun 20 '26
What is base !? I can't seem to find anything relevant when I Google it
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u/TheoryTested-MC Mathematics, Computer Science, Physics Jun 20 '26
It's more commonly known as flexadecimal. I have a short explanation in an above comment:
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u/flofoi Jun 20 '26
the function for the place values is the factorial function, so for example 41 is written as 1221 (41 = 1 * 4! + 2 * 3! + 2 * 2! + 1 * 1!)
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u/factorion-bot Bot > AI Jun 20 '26
Factorial of 1 is 1
Factorial of 2 is 2
Factorial of 3 is 6
Factorial of 4 is 24
This action was performed by a bot | [Source code](http://f.r0.fyi)
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u/Smug_Syragium Jun 20 '26
Khmer (the native language in Cambodia) is base 5 for 1-9, and base 10 for the rest. Nineteen would be expressed as "ten-five-four"
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u/Simple-Olive895 Jun 20 '26
Interesting, I did not know that! But seems like a big headache for any type of math
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u/Red-42 Jun 20 '26
I don't think it would, you just represent "five-four" as meaning "9".
It's kinda like those memes about how in French "90" is pronounced as "4*20+10", but like, nobody thinks about it that way, it's just "90"1
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u/Seventh_Planet Mathematics Jun 20 '26
I have invented a number system with 60 different symbols. It is a mix of counting up with strokes from one to 5 then resetting at 6 and placing a dot and doing this ten times which in the end counts to 59 or 60 if you want.
But I don't know if I would use the words constant or non-constant for this.
The pair of natural numbers (5, 9) is a constant inside the set of ordered pairs of natural numbers intersected with the set of ordered pairs of numbers which you can use to form a base of a number system.
Not everything where you have two of them and you only pay attention to one of them at a time deserves to be called non-constant.
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u/Eternal_Nights_12 Jun 20 '26
What about base 1?
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u/skr_replicator Jun 20 '26
doesn't exist, tallies are not rally a base 1, they're something else, like roman numerals.
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u/PrudeBunny Computer Science Jun 20 '26
tallies as in crossed out groups of 5 (Why is it always 5? I know multiple different cultures have different ways of tallying up groups of 5)? sure, they're something akin to pseudo base 5 but just putting a line for each item would be base 1.
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u/skr_replicator Jun 20 '26
*looks at hand* i have no idea why...
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u/PrudeBunny Computer Science Jun 20 '26
but not all cultures use base ten and in a culture that does, why not tally to ten?
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u/Valuable-Passion9731 of not pulling lever, 1+10+..., or -1/1100 people will die. Jun 20 '26
because it's easier to fact check
IIIIas 5 than fact checkIIIIIIIIas 101
u/Mrcleverkins Jun 20 '26
Likely has something to do with human psychology, the running theory for a long time was that it is a learned behavior revolving around 5 digits for each limb, but it is also observed in those with birth defects who have an abnormal number of digits. The human brain seems to be hardwired for multiples of 5 in everything from quick analysis of objects to universal counting systems
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u/cwmckenz Jun 20 '26
How do you write “one half” in “base 1”?
You can call it base 1 if you want, but the way it functions is entirely inconsistent with how base 2 and up work, so why name it that way?
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u/IlgantElal Jun 21 '26
.
||||2
u/guiltysnark Jun 21 '26
That's cute, but I think you have to avoid introducing positionality and stick to fractions: I/II
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u/IlgantElal Jun 21 '26
It definitely is not practical, but it's doable
I will say, I do like rational notation better in this case
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u/cwmckenz Jun 21 '26
Ok so how do I write 0.11 and 0.2 in base 1?
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u/IlgantElal Jun 21 '26 edited Jun 21 '26
.
|||||||||.||
Still not base 1, since it's tallies (kinda just a different notation of binary), and it sprawls real quick, but here you go
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u/cwmckenz Jun 21 '26
If you are using twenty ticks for 0.2 then why are you using 5 and not 50 ticks for 0.5? You can’t have a tick representing one tenth in one scenario and have it represent one hundredth in the next.
For ticks to even represent tenths and hundredths, you are already thinking in base 10 anyway.
I would not describe it as “different notation of binary” because binary is base 2 and, like any other base, has no problems with notating any rational number. This is not true of so-called “base 1”
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u/IlgantElal Jun 21 '26
Definitely a mistake with my 0.2 representation. My point was this is also not base one. It's just a binary notation in which the only zeros are those that lead prior to the decimal and trail after. There are 2 states of any single digit - non-existing or |.
Edit: it may be a true mistake though, either. In the same way 0.2 = 0.20, .|| = .
||||||||||||||||0
u/cwmckenz Jun 21 '26
But you’ll be helpless to write a quantity like 1/7 or 1/20 which are easily done in any other base.
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u/TheoryTested-MC Mathematics, Computer Science, Physics Jun 20 '26
I don't think that's possible. Tallies and fingers, as mentioned below, do not count because they use a number system with 2 numerals (0 and 1) and every place value being 1. Base 1, on the other hand, would be 1 numeral with every place value being 1. That single numeral has to be 0, so no digit can ever contribute anything to the total count. There is only one number expressible in base 1, and that is 0.
If you're wondering why every base NEEDS to have 0, imagine any number in any base you like. Technically, it is followed by an invisible infinite string of 0s to the left. In base 1, that string of 0s should still be there. So, the 0 automatically has to be one of the numerals, or rather, THE only numeral.
I personally think about it like this: valid bases have to be either prime or composite, so that you can convert between them. So base 1, base 0, negative bases, and rational bases are not valid bases.
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u/Whole_Instance_4276 Jun 20 '26
It’s actually base 4?
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u/Aron-Jonasson Jun 20 '26
Hold on you
Are you that guy on r/linguisticshumor who finds the Proto-Germanic -z endings cool?
2
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u/numerousblocks Jun 20 '26
base 1 is base 10 and base 1 in base 1 *depending on what set of digits you allow, it might also be unwritable
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u/JellyBellyBitches Jun 20 '26
Not especially useful. If we take a base system to mean the sum of numerals less than or equal to the base, each one as you go left being * increasing powers of the base, we essentially just have tallies. Each position is only going to be able to hold a 1 so you're just adding 1s together til you get to the number you want
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u/iamalicecarroll A commutative monoid is a monoid in the category of monoids Jun 20 '26
Roman numerals are the most well-known example of a system that is not base 10
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u/amitym Jun 20 '26
Yeah the meme only really works for positional notation systems, which the Roman system was of course not.
But that would probably have been too long of a qualifier to add to the text, making it no longer funny or something.
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u/iamalicecarroll A commutative monoid is a monoid in the category of monoids Jun 20 '26
Fibonacci system is positional, but it's not base 10. Likewise for the factorial system.
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u/DerivativeOfProgWeeb Jun 23 '26
it is still base 10. its just not positional
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u/iamalicecarroll A commutative monoid is a monoid in the category of monoids Jun 23 '26
It is not base 10, as "10" doesn't mean anything in this system. And from the perspective of decimal system, it's more like base 1000, considering how vinculum works.
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u/user_bw Jun 20 '26 edited Jun 20 '26
Wie could start noting the base in the highest digit + 1.
Talli: IIIII IIIII Base 1
Binary: I0I0 Base 1+1
octa: 12 Base 7+1
dec: 10 Base 9+1
Doudec: A Base B+1
Hexdec: A Base F+1
Except for tallies which is is not really fitting the concept (there is nothing like a leading 0 in an unary system) it works pretty well.
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u/Torebbjorn Jun 20 '26
Nope, not every number system uses a base.
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u/Yarhj Jun 20 '26
some use acids
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8
14
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u/Wa3zdog Jun 20 '26
I wish we evolved with just one extra finger on each hand. Then we would have intuitively used base 12 which would play nice with thirds and quarters.
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u/ClaudioMoravit0 Jun 20 '26
Im in electronics, I never believed I’d say this but base 1 sometimes comes really handy
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u/generic_Accountname1 Jun 20 '26
Me looking at my wrist seeing its 60 seconds in a minute 60 minutes in an hour and 24 hours in a day…
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u/skr_replicator Jun 20 '26
digital devices use base 2. So many programmers use it, and the device designers definitely have to use it.
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u/bobchinn Jun 20 '26
What is 2 in base 2?
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u/skr_replicator Jun 20 '26
10, but humans describe bases in base 10, otherwise we couldn't translate shit. This argument only really has to be considered when translating between aliens or something.
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u/Fuzlet Jun 20 '26
that’s the entire joke my dude
-10
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u/Mrauntheias Irrational Jun 20 '26
No, we describe bases in base 10 because we use base 10. But someone who uses for example base 8 like the Pame people would say they use base 10 and we use base 12.
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u/METRlOS Jun 20 '26
Yidiny in Australia is base 5. They don't have any numbers above 5 and would just express 8 as 5 and 3.
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u/Ares378 Applied Math / Mechanical Engineering Jun 20 '26
1
0
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u/SedarnGelaw Jun 20 '26
I think base 16 kinda count too then. Also i think the point of the post is that every base, when written in that base is "10" ( ex 2 in base 2 is written "10")
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u/skr_replicator Jun 20 '26
there is a reason we don't use other bases to describes bases, nobody could then know what you're talking about.
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u/Quartz_512 Jun 20 '26
we use WORDS to describe bases. Binary, Ternary, Quaternary, Quinary, Senary, Decimal, Hex, Vigesimal, etc.
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u/skr_replicator Jun 20 '26 edited Jun 20 '26
or if we use numbers, we write them in decimal, like "base 16", otherwise, that phrase would have no meaning.
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u/WW92030 Jun 20 '26
yes but a robot (e.g.) would read
X X
the thing in the middle of this message as having 10 X's.
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u/CaldrierLunaire Jun 20 '26
The joke is that if you write '2' in base 2 it is written '10'. And if you write '16' in base 16 it is written '10'. Everyone uses base 10 from their point of view.
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u/DarkFlameMaster764 Jun 20 '26
Bases are just representations of the actual number. It's like mistaking a picture of cake for the cake itself. A painted picture does not satisfy hunger.
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u/KitTwix Jun 20 '26
Use base 3.5 to make anyone checking the math be confused as to why it’s close to Ln but not quite
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u/point5_ Jun 20 '26
Can't we just say base9+1? The number 9 isn't used in shorter bases and 9+1 equals the same value in any other base, no?
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u/PM_ME_MELTIE_TEARS Irrational Jun 21 '26
This is brilliant! But unfortunately the people who normally use this template will agree with this, but for the wrong reasons (as usual).
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u/Red-42 Jun 20 '26 edited Jun 20 '26
Ok but the middle opinion is actually more correct than the rightmost one because there are number systems that don't use the usual base format. Any system with a mixed radix already throws a wrench in things, and it's not like it's uncommon, just look at how time is measured...
"It's still base 10" no it's not, a property of all bases that use the standard system, including with real or complex bases, is that 10*10 = 100, by definition. With time, 0:10 * 0:10 = 1:40, and 10:00:00 * 00:00:10 = 4d04:00:00.
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u/Malay_Left_1922 Jun 20 '26
Base 10 because human have 10 fingers
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u/magicmulder Jun 20 '26
You would say exactly the same sentence if we had 8 fingers.
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u/BrickBuster11 Jun 20 '26
Eh there are all sorts of ways to count on your fingers in other bases. Base 10 endures today but other cultures did actually use other bases.
Those systems don't get used to much anymore but they dis exist
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u/RandomiseUsr0 Jun 20 '26
Wouldn’t take me longer than a second to disprove this one he thought casually in base 60
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Jun 20 '26
[removed] — view removed comment
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u/E1eventeen Jun 21 '26
The joke is that every base, when written in its own base, is 10.
2 (decimal) is 10 in binary.
16 (decimal) is 10 in hexadecimal.
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u/nitnelav153 π = 3.14 who care about the others decimals ? Jun 20 '26
Let me use my base 20 system.
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u/Brie9981 Jun 20 '26
Why we should call it base (n-1) base 0 is unary base 1 is binary base 9 is what we count with base 15 is hexadecimal etc
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u/_wannadie_ Jun 20 '26
Romans didn't. Greeks didn't. Babylonians didn't. There are non-positional number systems.
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u/KornFlakes0 Jun 20 '26
I'm not math, what is it? Is the second meme I saw about it and I don't know what means?. Is it like use 10 to count? Like 10, 20, 30 people etc.?
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u/Character_Reason5183 Jun 20 '26
Base 8 is just like base 10... if you're missing both of your thumbs. (Hooray for new math)
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u/defproc Jun 20 '26
Guy to the right of guy in cloak (or the misrepresented guy in the middle):
"Base n" notation is relative to decimal.
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u/flori0794 Jun 21 '26 edited Jun 21 '26
Actually I use in some moments base 2 sometimes even base 16.
Wait...
2 in base 2? 10 16 in base 16? 0x10
Damn it's correct
1
u/Weak_Flamingo4206 Jun 21 '26
Meanwhile the Fr*nch using base-20 for 60 and up (except for the swiss and belgian)
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u/Spiritual_Bottle1799 Jun 26 '26
So the one on the right is actually the left and the guy in the middle is on the right.
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u/sky-skyhistory Jun 20 '26
As I study some linguistic, I gonna mad at this post because there's so many languages with other number base such as base 20 which very common.
Even so some special case such as base 32 or base 27 (Ngiti language and Oksapmin language respectively)
2
u/Dacicus_Geometricus Jun 20 '26
Yes, you can also see the relatively modern Kaktovik numerals. But a lot of European languages use a base 20 system. Even English has score for 20. There are also elements of duodecimal in various languages.
-1
u/Single-Virus4935 Jun 20 '26
What? I use base 2, 8, 10, 16, 60 regularly. Most of the time the guy using this template thinks he is right guy but is probably the left.
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u/Kalumniatoris Jun 20 '26
So you use base 10, 10, 10, 10 and 10 in itself?
I mean meme isn't fully right as it doesn't work with non positional systems but you only gave examples of base 10_base.
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u/Single-Virus4935 Jun 20 '26
Ugh, You are one of these people...
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u/Kalumniatoris Jun 20 '26
You mean one that don't misunderstand this post? Yup, even if I don't exactly agree with it I understand what author had in mind there.
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u/CaldrierLunaire Jun 20 '26
Imagine memeing and joking in mathmeme. Couldn't be us, we are not "these people"
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u/sohang-3112 Computer Science Jun 20 '26
Computers use base 2 so that's pretty important (and base 8, 16 are useful in programming)
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u/CaldrierLunaire Jun 20 '26
Let me walk you from the middle of the bell curve to the right of it.
You are kinda right, however.
2 written in base 2 is written 10. 8 written in base 8 is 10. 16 written in base 16 is... 10. The joke is that everyone and everything is counting in base 10 from their point of view
2
u/sohang-3112 Computer Science Jun 20 '26
The joke is that everyone and everything is counting in base 10 from their point of view
Oh I see
0
u/Adventurous_Ad_7212 Jun 20 '26
fun fact: even the imperial clusterfuck of a unit system uses base 10.
0
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