![b10[1].jpg](https://i.imgur.com/3tvT8kU.jpg "b10[1].jpg")
What do you think about base 10?
Do you think there's a better base to teach math with?
What would be the worst base to teach math with?
I always thought a base that you could divide by 2 easily would be good, like 16.
In this hypothetical assume we are not used to any base system yet.
>>7882226
>Do you think there's a better base to teach math with?
No, we have 10 fingers.
The best base is base 12, because it is small enough and 12 can be divided by 2, 3, 4, and 6, while all the numbers bellow 12 have at most two divisors.
>>7882238
Actually, now I remembered that 12 is as good as 10 for teaching. You can use these things on your hand, dunno how they are called.
>not using base 2 and teaching kids how to count to 31 on one hand
>>7882226
i only do math in base e
>>7882258
No you retard. The only reason for picking a certain base is making division easier so that our daily lives are easier. For mathematics the base doesn't matter.
>not using base P where P is the product of all primes
>>7882271
>make ridiculous claims
>call people who ask for evidence retards
you still haven't provided any reasons for this divisibility criterion in math or any studies on the benefits of teaching with base 12, retard. if anything, I'd say a prime base is better.
>>7882284
>you still haven't provided any reasons for this divisibility criterion in math or any studies on the benefits of teaching with base 12, retard. if anything, I'd say a prime base is better.
How the didn't I provide reasons? It makes division easier. The easiest from all bases bellow 12. Why the fuck would pick a prime base for everyday life? It makes division more complicated than non-primes.
>>7882283
You mean base 4\pi^{2}
>>7882284
Are you stupid or what?
Here:
https://www.reddit.com/r/askscience/comments/1wx004/what_are_the_advantages_for_a_base_12_system/
https://www.youtube.com/watch?v=U6xJfP7-HCc
>>7882226
>I always thought a base that you could divide by 2 easily
Multiply by 5 and shift the last digit right
I say base 16. Binary is more fundamental and the basis for much of our technology, but all 2^n bases are really just shorthand for binary, at the expense of more symbols to learn. I think 16 probably strikes the right balance for processing information fastest.
>>7882226
base 9
>>7882333
Do you really think that's easier?
16
8
4
2
1
0.8
0.4
0.2
0.1
0.08
0.04
0.02
0.01
0.008
0.004
etc.
Compared to:
10
5
2.5
1.25
0.625
0.3125
0.15625
0.078125
0.0390625
0.01953125
0.009765625
0.0048828125
0.00244140625
0.001220703125
0.0006103515625
0.00030517578125
0.000152587890625
0.0000762939453125
>>7882398
I fucked up, the 16 at the top should be 10.
>>7882226
>base 10
It's pretty neat. Product of 2 distinct primes. The 10 finger argument probably works for the less math inclined.
>Better base
Not really, but look to the logarithms and you'll notice that there are useful qualities to be found.
Base 6 is also neat. You can represent 35 on your two hands. Primes always end on 1 or 5 (except for 2 and 3).
>base that you could divide by 2 easily would be good
Sure, just look to computer science.
>>7882430
Why is being a product of 2 primes a good thing? Wouldn't that make it a bad thing? Less divisible?
>>7882436
Not at all. By having distinct primes you get more fractions that are easy to operate with.
This is sort of the argument for 60 X in Y like time.
Half an hour, third of an hour, a quater, a fifth or a sixth. All of the are easy to calculate.
Now how about if the hour was 64 minutes instead? Most of those fractions mentioned earlier would no longer make sense. Sure 1, 2, 4, 8, 16 and 32 minutes could be useful, but what I think would happen instead is that one would think in binary about the whole day. Use binary fractions and there would be 16 or 32 fractions that would be considered much like the hours we use today.
Still it would not fit with the year. lunar cycles or anything else people would try to use the number system of choice for.
Also why isn't time metric yet? Days in a year has a reason of course, but why not units of measurement like 1 day / 10, and that unit / 10, etc. We do it like that for 10, 100, 1000, years etc.
>>7882436
Composite bases also mean that you can tell a numbers divisors in that base if the number is made up of the same primes the base is made up of.
>>7882263
> mfw my radix economy is maximized
https://en.m.wikipedia.org/wiki/Radix_economy
People underestimate how easy it is to learn symbols. For everyday use a system that's 100 symbols or so would be best because then numbers would only be a few digits long. Even bigger numbers. Having learned 3k+ characters in Japanese fairly easily I can tell you it's not as hard as it sounds. You do it all the time with whole words in English.
>>7882705
Hey, I have a great idea! Since 100 very unique looking symbols is pretty hard to do (u vs v, I vs l, h vs n), why don't we have each of the hundred symbols be made of a combination of two sub-symbols? Then we can have a base 100 but only need 10 symbols. For example, 7852 could be 78 52 in this crazy new base!
>>7882721
>100 unique looking symbols is hard to do
>>7882724
0 vs O vs o vs Q, and thats just 26*2+10=64 symbols. Plus alot of capital letters are just bigger versions of the lowercase, while you would need a brand new symbol. You couldn't have a number like oO01Ili or xXsS.
Also, you wouldn't be able to copy letters for your new numbers so you would need 90 simple symbols that can't be mixed with other symbols even with messy doctor writing. Just writing 21 or 87 or 32 is much less troublesome than having the risk of mixing up complicated symbols.
>>7882741
Cyrillic alphabet?
Personally, I prefer the unary base. It's so simple and makes calculations much easier. For example, llllllll is 8, while llllllllllllllllllllll is 20. It's easy to add, you just concatenate the two numbers, name any other base that can do that. Division is easy, as is multiplication. This base is also wonderful for finding remainders fast. lllllll/lll is ll remainder l. Plus you don't have to remember alot of complicated symbols.
>>7882751
Vast majority look similar to english letters or numbers, plus any unique ones like the second to last one is just as difficult to write as any two regular numbers.
>>7882741
So then why does Chinese have thousands of characters in use?
>>7882837
By having each character be extremely complex. It's am overall shitty writing style that shouldn't exist in the modern age. I'd much rather write 2 simple characters than 1 complex one.
Pic very related
>>7882754
ll cool llll school!
>>7882636
>Also why isn't time metric yet?
The SI unit of time is the second. So technically it is. An "hour" is 3.6 ks, etc.
(We don't use a day as the standard because a day is the rotational period of the earth, which is actually changing.)
Technically aren't all bases base 10?
Base "10": 0,1,2,3,4,5,6,7,8,9,10 -> base 10
Base "2": 0,1,10 -> base 10
Base "6" : 0,1,2,3,4,5,10 -> base 10
>>7883177
u made me lulz
>>7883177
No, you can define a base by how many digits are used until you need an additional digit next to it.
Denary: 0,1,2,3,4,5,6,7,8,9,10,11,12 etc.
Notice how an additional digits appears to the left when the digits representing the highest value resets? The same happens to binary
0000
0001
0010
0011
0100
0101
0110
0111
etc.
And the same with Hexadecimal:
Den. Hex.
0 0
1 1
2 2
3 3
4 4
5 5
6 6
7 7
8 8
9 9
10 A
11 B
12 C
13 D
14 E
15 F
16 10
etc.
>>7883346
I don't think you understood what he was saying. In "base-16" the number 16 (the base) is represented by the characters "10" so in base-16 you would say "I use base 10". You can say "I am using base 10" no matter what base you use.
>>7883354
Of course if you SAID it you wouldn't pronounce it "base one-zero," so there is no ambiguity.
>>7883354
Imagine you have X amount of water melons, now if I asked you to tell me how many there are, you can answer in any number base and it would mean the same thing, he just needs to remember that maths is a language, when you say number 15 in base 16 is 10 in base 10, all you are doing is translating it, like someone translating French to English.
>>7883407
>maths
stopped reading
>>7883427
>Getting butt hurt over something on the internet
Isn't 4chan outside of your safe space?
>>7883346
If you grew up learning hexadecimal the series 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F has 10 numbers in it and you would therefore refer to it as "base 10"
>>7883360
You do realize 10 is pronounced "ten" no matter what base you use right? This is where the ambiguity arises from.
>>7882226
Base 2 is the easiest to teach with:
Addition is repeated pairing
Multiplication is repeated doubling
Exponentiation is repeated squaring
Any 5 year old would rapidly understand arithmetic far faster than base 10 with all its annoying cases. Well any kid except for the future CS kids, they're just hopeless and will never learn math no matter what you try....
>>7883741
But of course it's not realistic because the strings would be longer and easier to fuck up reading (often having 5 1's in a row or something, reading it as 4 or 6).
>>7882636
ThIs did exist at one point while the metric system was being developed during the French Revolution. Each month had 30 days, divided into 10 day weeks. There were 5 complementary days which acted as national holidays. Every day was made of 10 hours, each with 100 minutes, each with 100 seconds. The length of a second was shortened as a result.
>>7882226
10 is the best cuz you have 10 fingers and thats all the math most people need to know
>>7883744
Binary is only 3.32 times longer which is actually a GOOD thing when teaching it to kids. 100, 1000, 10000, 100000, 1000000 quickly become very difficult to visualize (even for grown adults) but 4, 8, 16, 32, 64 are still comprehensible and easily visualized.
We should use base 0.
>>7883177
Yes, the name of any base system in that base system is "base 10".
Base six.
>Highly composite number so basic arithmetic is easier
>Can count to 5 on one hand, then use the other hand to represent the 10s place
>This allows you to count to what would decimally be 35 on your fingers, or 55 in base-6
Base 12 is good too, but finger-counting is a bit trickier and definitely more difficult to gesture.
Base [math] - \frac{1}{12} [/math]. We would be able to represent infinite numbers.
>>7884069
[math]baito-desu\sim[/math]
>>7883714
We get it, its just semantics so no one cares. We just call them base "6" base "2" base "whatever" because we are using the reference frame of our current base 10 to discuss them. Of course if we grew up with any other arbitrary base, we would call that one base 10. If we just referred to every base as base 10 there would be no distinguishable discussion to have.
>>7884065
This argument seems the most practical to me so far.
