Well, what would you call 10 if it were base 8? I always assumed it was just “ten” as in one, two, three, four, five, six, seven, ten, eleven…
Surely if you see 137 in base 8 you’re going to call it either one-three-seven or one hundred thirty seven, and not try to convert it to base 10.
You can’t call it “one hundred” anything. “Hundred” means ten tens. Obviously, not applicable here.
“One-three-seven” is better. Best is “ninety-five.” 
You can always say <number in decimal>-base-<number of base>. At least that’s what I do and no one bats an eye. The only time I don’t do this is in bases with alternative symbols (i.e. 1A in hexadecimal is just one-eh, though I suppose 10 would be ten-base-sixteen, or ten-hex if I’m being short and I’m certain we’re not working with base 6 anytime soon), or when there’s a rather long binary number (101010101000001110010101) in which case I just point to it and say “that number!”
My eyes are batting furiously. It’s a matter of convention, I suppose, but I just can’t bring myself to consider the word “ten” as anything other than “The number of asterisks here: **********”, and similarly for “hundred” and “twenty-three” and so forth.
I mean, not that appeals to a dictionary are conclusive in this matter, but I doubt you will find anything there defining “ten” as “The strings of symbols ‘1’ followed by ‘0’” or “the base in which one is working in a positional system of numeric notation”; rather, it seems to me to refer to a particular numeric quantity primarily, and its association with that string of symbols “10” is secondary, mediated through the common convention of decimal representation, but lost and irrelevant in any other base, or, indeed, other methods of representing numbers.
I think the problem here is that it is purely a visual joke whose point is missed when spoken – much like trying to relate a homonym joke orally; it’s the spelling that makes it funny and you can’t convey that aloud – at least, not without ruining the joke by explanation.
However, conventionally binary digits are spoken individually; one-zero-one-one-zero, etc., as with other base methods other than decimal. (Although with hex, I say numbers not containing letters as their decimal counterpart, and numbers containing letters individually. But that’s just me.)
I can’t tell if you understand this far better than I do or if you’re really confused.
Oh. Well, what would help distinguish between the two?
Not sure.
But here goes. Most people are accustomed to base 10. We have 10 numbers: 0,1,2,3,4,5,6,7,8,9. Once we reach 9, we’ve run out of numbers. So we add a digit and make a new number: 10.
Binary is base 2. The only numbers available are 0 and 1. 0, 1…then we run out. So we go to 10.
So ‘10’ in base 2 isn’t ten. It’s what we’d call “two” in base 10. So the bumper sticker is really saying “There are (two) kinds of people,” but it’s expressing two in binary.
Binary is the language of computers, all 0’s and 1’s. Or, if you will, electrical switches are either on or off.
BTW you could have any base you want. Hexadecimal is a biggie in programming I guess. The numbers are 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F…10.
Other, more advanced mathematicians will be along to explain (and correct me) if you’re interested.
You’re all a bunch of 733+15+5 to me.
I don’t mind being insulted mathematically, so long as you explain it to me.
Math cartoon for today:
He is calling us elitists (or, rather, “leetists”) in leetspeak.
And who is i to tell π to be rational? But I suppose it’s much harder to work “Gaussian rational” into a pun…
I once played on a softball team where we got to choose our own numbers for our jerseys. First I requested π and it was no deals. Then I requested sqrt2, but no deals again. i? Nope. I ended up choosing 00. I figured when I ran on the field people would say “OO!”
ETA: I haven’t been in a math class in 20+ years. Did my explanation pass?
Sure. I pretty much agreed with all of it; the one thing I would claim in addition is that ‘10’ in base 2 isn’t just what we call “two” in base 10, but also what we call “two” in base 2, “two” in hexadecimal, “two” in Roman numerals, in tally mark notation, in p-adic representation for any prime p, etc. Whereas the string of digits ‘10’ refers to different numbers depending on which base of a positional system of numeral representation one uses [and on whether one reads the most significant digit as the leftmost or rightmost one, etc.], I would say that the expression “two” refers to a particular number completely independent of such choices, always referring to “This many: * *”.
Does that make sense?
(Of course, the example of “two” isn’t very illuminating, since almost all bases express two via the same one-digit representation. But everything I said holds just as well for “ten” and “twenty-three” and “hundred” and so on.)
As the math professor said to his lovely intern, after they had become mutually enamored with one another, b4i4q (ru/18) qt∏ ?
Yes, pretty much (not sure what p-adic is).
It’s at the heart of the question, right? The bumper sticker would be cool to use when telling jokes among mathematically-oriented people. But I’ve never heard it spoken. As stated earlier, I guess this is a joke that works visually but not verbally.
Bad…that’s just bad.
p-adic is a lot like base p (so much like it that perhaps it was superfluous to bring it up in this context), but instead of having a finite string of digits before the “decimal point” and a potentially infinite string after, it has a potentially infinite string of digits before the “decimal point” and a finite string after. The calculation rules of arithmetic are basically the same, though, so that, for example, in p-adic with base 5, say, we would have that …444444 + …444444 = …444443 [since 4 + 4 = 13, which is to say, 3 with a carry of 1].
So, as that example shows, …4444 satisfies 2X = X-1, telling us that …4444 = -1, A nice thing about the p-adic representation, then, is that negative numbers are represented in basically the same way as all others, with no special negative sign needed or any such thing. If you use a prime base p, then you get numbers which act like all rationals and, indeed, all reals, so that the system is fully adequate for all the usual purposes.
Anyway, this isn’t a terribly detailed or useful description yet, but hopefully it at least stirs some interest.
Sorry, I shouldn’t have said “all reals” (e.g., the 2-adics don’t contain a number acting like sqrt(2)). Rather, the system acts like the system of all reals in many ways, though also differs in some important ones.
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