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Why do we call it "Base 10"?
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Why do we call it "Base 10"?
Shouldn't it be called "Base 9"?
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>>7651181

The numbers are modulo 10
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>>7651181
starts at 0 bro
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>>7651181
Do you think binary is "Base 1"?
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>>7651195
Yes. I do.

1 is the last number in the radix. Why would I describe binary as "Base 2" when "2" doesn't even exist in binary?
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>>7651181
There are ten symbols, 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Hence it is base ten.

Note, it is not base 10, as every base is base 10.
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>>7651199
>>7651203
>Why would I describe binary as "Base 2" when "2" doesn't even exist in binary?
The symbols are irrelevant. You can use 'a' and 'b' for binary, that wouldn't make it "base ba". It would still be "base 2" operating under the common convention that numbers not otherwise marked are base 10. There are scenarios where this assumption breaks down, but it is not very difficult to manage.
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>>7651203
>Making a distinction between 10 and ten
This is just a lie mathematicians say to make themselves feel better about the fact that the nomenclature for bases in inherently faulty and unnecessarily reliant on a base 10 system for a frame of reference.
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>>7651181
all bases are base 10.
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>>7651181

Am I the only one who's going to point out that, despite the quaint imagery, this children's book-account of futurefraud is a very good one? The only factual error is the suggestion that "computer crime" would become harder over time, when the opposite is the case, but fortunately they don't state it as a fact.

9/10 late 70's/early 80's account of "computer crime", would recommend.
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>>7651208
>>7651208
Why would you use "a" and "b" though?
Would you ever use a system in which "9" and "2" represented "1" and "0" respectively? I mean, you could, but it'd be extremely poor form to do so.

The symbols obviously do matter, especially if we're going to be consistently translating them between multiple bases. Using symbols that are commonly used in other conventional bases just leads to confusion. Using your "a" and "b" example, I could just as easily assume that you're using hexadecimal. Or variables.

Why shouldn't we have a standard by which symbols are ordered so that conversion is easier across multiple systems?
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>>7651237
>Why would you use "a" and "b" though?
Why would people use TRUE and FALSE though?
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>>7651215

>the symbols obviously matter
Not that guy but apart from arbitrary conventions which aid human cognition itself --- no, they (the symbols involved) don't matter.

Your suggestion for a standard for representation of bases is completely reasonable. In fact, it is so reasonable, that we already have a modern convention for the representation of a number base up to, oh, say, 36: 0-9-A-Z. You'll always need to know context in any mathematical representation though, so you just need to git gud (this only really crops up with hex in contemporary contexts).

If you really want finitely more symbols, you could use cuneiform:

https://en.wikipedia.org/wiki/Sexagesimal

But of course what you're really getting at would require arbitrarily many numerals which we can simply describe as a_n or similar, where n, of course, is a base-ten number or whatever base we're most comfortable with. :^)

>>7651209

This is a dumb post, and the whole crux of OP's troll was employing the English language phrase "Base 10", as opposed to "Base ten". The only reason why you think what you think is because you're so used to working with "Base ten". If you were to actually git gud, then you would understand that your argument is spurious. Once again, the symbols are immaterial.

----------

Both of you would do well to look up the Basis Representation Theorem. If you even want a book with it, look for Number Theory-Andrews (Dover), section 1.2 (right at the very beginning!), which can be had for under \$(20)_10 at the average brick-and-mortar or your online bookseller of choice.
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There are ten elements, from 0 to 9.
In base two there are two, 0 and 1.
In base sixteen there are sixteen, from 0 to F.
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>>7651181
Identifying counting systems by the number of digits contained in the radix is inherently faulty. Because of the inclusion of 0, the number used to identify the radix is always one greater than the final digit in the radix itself. Under a base 10 system, this always requires the use of either multiple digits from within the radix itself or the use of digits not contained within the radix at all.

This can be alleviated by recognizing an objective radix that lies outside of all conventionally used bases, composed of an ordered set of every internationally recognized set of letters and symbols.

Therefore, every base should be referred by the final digit contained within it with respect to this objective radix rather than digits explained through other conventionally used bases.

Base 10 is base 9.
Base 16 is base f.
Base 2 is base 1.
And Base 1 shouldn't even be recognized because Base 1 is fucking stupid, fuck Base 1.
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>>7651281
Fuck you, base 1 is pretty much how counting started, which is how math started.
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>>7651287
Base 1 is fucking dumb and doesn't even have any way to represent zero.

You can barely even call it a radix considering it literally has only one number in it; itself.
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>>7651617
>doesn't even have any way to represent zero.
Sure it does, a blank space. Or alternatively, (1-1).
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>>7651617
A radix of one still counts. After all, we can divide by one, can't we?

>>7651630
I find the idea of representing zero with a blank space to be highly amusing and endorse it wholeheartedly. It makes sense that you can count to zero by not counting at all.
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>>7651630
>>7651650
The whole point of having a radix is to demonstrate higher numbers in abbreviated terms.

Counting in a system of 1 completely defeats the purpose of having a radix in the first place. It's total fucking shit, and there's a good reason why it's rarely ever recognized to begin with.

>Or alternatively, (1-1)
You're using 3 fucking digits to describe a single concept. This is counterproductive at its core. And as cute as you think using a blank space is, it still means you're using a system that can't be adequately converted to any other base system neatly.
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>>7651281

This whole train of thought is still as spurious as it was in your earlier post >>7651209 , which may be recognized as the same person by repeated use of the phrase "inherently faulty". Nothing is "faulty", you just don't like the current arbitrary convention, possibly because you yourself become confused when performing base conversions, and so you want to replace one arbitrary convention with another (your own), which would not amount to doing anything mathematically substantive, and would carry over its own issues per your own headache-inducing wish to define an "objective radix" that requires every written character set ever. Second, you haven't appreciated the simplicity and mathematical substance of the simple act of tallying a.k.a. "base 1", which although tedious, is in a sense the most honest way of counting.

Third, your confused thinking continues when you mistake a numeral for a number by using the latter word in the post >>7651617 . a) It is clear from reading your own words why you have this confused thought process. You see value in using conceivably finitely many disparate RL written characters to "attack" the problem of number base, when of course a number base may call for arbitrarily many characters, and so is best treated of in a general case by means of simple algebra and not by opening up every font library ever. What a terrible idea that was. And b) , you reject a distinction between numeral and number, which is what leads you on your own wild goose chase in the first place.
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>>7651181

but to humor the troll
base-X numbers are computed by doing the following:

for each ith digit, multiply the digit by X^i (hence why it is called base-X) and add these digit products together

for base-10 let's say the number is 19237
the base you use to compute this (in a non-based concept) is 7*10^0+3*10^1+2*10^2+9*10^3+1*10^4 = 19237
notice the
>base is 10
you fucking dumb ass

sage

every

field
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>>7651778
>and would carry over its own issues per your own headache-inducing wish to define an "objective radix" that requires every written character set ever.
As far as I'm concerned, my train of thought is more or less an inevitable conclusion.

If you're going to have an organized set of every universally recognized character known to man, you might as well order it. And while you're at it, you might as well use the ordering as a standard to develop a radix.

It really, really isn't that hard. We already have computers that do this very thing on a regular basis with stored databases of characters.
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guise guise
what if
guise
What if we used a function as a base instead of a constant?

I'll take my fields medal now.
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>>7651801
The funny thing is that you haven't actually invalidated anything I've said.

You might think you've had, but all you've done is make it clear that you don't actually understand the criticism I'm making in the first place.

First of all, base-10 is a fucking garbage system, and not one that we should be using as a standard by which all other bases are compared to.
Second of all, defining a base by integers that don't exist within it is recursive and stupid.
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>>7651237
so you want the common bases to be in different symbols:

[0,9] reserved for base 10
[a,b] reserved for base 2
[c,j] reserved for base 8
[k,z] reserved for base 16

so:

1 in base 10 = 1
1 in base 2 = a
1 in base 8 = c
1 in base 16 = k

and then we have no way to represent uncommon bases
like what the fuck gives you these retarded ideas?
can you just finish freshman year before opining on everything that your former computer SCIENTISTS have laid out for you? fuck the arrogance is unbearable
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>>7651281
>I am a hipster faggot that contributes nothing to society or science, and yet I get mega pussy while stroking my own ego.
>p.s. I don't "believe" in zero.
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>>7651814
how have i not refuted your entire argument?
it's called base-10 because it is computed using 10 as the base
seriously what are you not getting?
regardless of it being a garbage system.
>defining a base by integers that don't exist within it is recursive and stupid
why would you use a base of decimals? and what makes you think 10 doesn't exist?

troll in all fields
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>>7651816
>so you want the common bases to be in different symbols:
No, no, and no, holy fuck no.
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>>7651227
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>>7651827
My argument is that the number 10 does not exist within the base 10.

In fact, the number 10 does not exist within any base. Ever. 10 inherently exists outside of every radix because it's a double digit number.
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>>7651181

>good luck
>i'm behind seven proxies
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>>7651808
>my train of thought is more or less an inevitable conclusion.
>I cannot distinguish between fact and my own opinion.
>I am a tremendous douchebag.
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>>7651834
>because muh dubs
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>>7651834
>My argument is that the number 10 does not exist within the base 10.
Your argument is both inacurate and invalid..
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>>7651834
wrong
the number "10" exists in every base just under a different representation
and hell if you're saying the representation can't vary then the value can and "10" still exists just under different values
every base can represent two digit numbers and if you don't get it, take it to you TA and stop shitting up
>muh board
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>>7651839
>fact
You don't even know the definition of "fact", faggot.

The naming schema for bases is conventional at best.
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>>7651849
You mean "true" and "unavoidable".
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>>7651855
>>7651834
>>7651181

OP is trolling

ignore all further posts

ignore all further replies
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>>7651855
>>7651834
>>7651181 (OP)

this is a bait warning
ignore all further posts
and ignore all further replies
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>>7651195
Of course not, it's "Base 10."
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>>7651855
>>7651834
>>7651181

ignore everything you see from now on and don't waste your time responding to this thread
>sage
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>>7651850
>every base can represent two digit numbers
You are absolutely, 100% correct.

But double digit numbers still do not exist within the set a radix. "10" does not exist within 0-9.
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>>7651866
>>7651868
>>7651871
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>>7651844
Checked.
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>>7651281
>>7651687
>dislike for base one

I respect your right to have differing opinions on this matter. Truly, I do. You can say that it is not a system you like, or that it is inefficient. You can say that it does not conform to the specifications of what you think a number system should be. I have no problem with this. I simply wish to remind you that base one is still a valid counting system, and one that some people happen to like for its inherent simplicity.

Nobody owns a monopoly on truth.
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>>7651801
>sage
>every
>field
>no sage in the name field
wut
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>>7651851
>The naming schema for bases is conventional at best.
And your convention is completely retarded.
Nine has nothing to do with base 10.
See, I DO know something about facts.
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>>7651919

underrated post but it's probably the same stupid guy (possible troll) who made this stupid post, >>7651834 which again shows that that he doesn't understand the difference between numeral and number so sage it anyway.
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>>7651931
9 has everything to do with base 10.

It's the final number before it rolls over.
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>>7651181
More like inbetween
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>>7651912
All I'm saying is that unary is considered a non-standard positional numeral system for a number of good reasons.

The fact that it sucks is a direct result of these reasons.
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>>7651937
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>>7651951

No, they (you) aren't. But enough other adults have been baited into this that you'll dig in and troll harder. saged again.