Re: In base 1, the number after 0 is:
by AppleFritter (Vicar) on May 01, 2014 at 11:43 UTC

Trick question! There's no number 0 in the usual sense in base 1, since you're just counting sticks, as it were. The role of 0 (the number, not the digit) is taken over by the empty string, and after that you get "", "" and so on (modulo your choice of symbol for counting).  [reply] 

I agree, but what is then consequently the meaning of the empty string in base n with n > 0 ?
:)
If one thinks it through its obvious that emptiness is a notation for skipped zeros ...
...i.e 42 is in reality 0...042 with an infinite number of leading zeros.
With the exception of the number 0 itself which isn't reduced to an empty string.
... well o_O ...
Lets talk about base 0 now ;)
Cheers Rolf
( addicted to the Perl Programming Language)
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0 is both a digit and a number (which I will call "zero" for the rest of this post to make this clearer), and I think it's important to keep that distinction in mind.
Zero can be represented in a variety of ways, including as "0". It could equally well be represented as "22", or "e^{iπ}+1", and so on; the number's the same, it's just written a different way. (Compare how "0.999..." denotes the same number as "1"; it's merely two different ways of writing down the same thing.)
"42" vs. "042" vs "0...042" with any arbitrary number of leading 0s is an example of the same. That's the digit 0 there, not the number zero; the number is the same (and canonically written as just "42", although that's just convention).
Indeed, for another example, compare different bases. 0x2A (hexadecimal) is the same as 42 (decimal) as 052 (octal) as 101010 (binary). Different representations again, but they are all names for the same number.
So that said:
I agree, but what is then consequently the meaning of the empty string in base n with n > 0 ?
The meaning of the empty string in base 1 is the number zero  but not the digit 0, though that digit, on its own and interpreted in bases n≥2, represents the number zero. The meaning of the empty string in such higher bases isn't generally agreed on, I think (by which I mean that nobody asked me for my opinion on the matter ;)). Consider this: you can tell me what "2+3*4" is, but if I asked you about "2+*4", you'd say that that's not a valid calculation, rather than giving the answer as "2" after having interpreted the empty string between the "+" and "*" as the number zero.
Lets talk about base 0 now ;)
Hmm, base 0? Talk about weird! Since 0^{0}=1 by usual convention, but 0^{n}=0 for any other n, you couldn't represent any number larger than one. But that'd be the least of your problems, since your set of symbols (read: digits) would be empty anyway, and you could not actually represent anything other than the number zero, which would be represented by the empty string.
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Exactly.
As to what was revealed to be the real question:
Hence, the poll question is really, what is the first representational digit in base 1
I think "1" is quite intuitive. prime factorization using base 1 reveals some of the benefits to working in base 1:
They don't have the arbitrary range limitations of Perl's regular number representations while converting between the two is nearly trivial. Plus finding prime base1 numbers is particularly compact code in Perl. And when the primality test fails you are also handed some factors! So base1 numbers are perfect for finding prime factorizations! They aren't very space efficient, unfortunately (hey, no one's perfect).
As well as providing handy Perl code for working with them.
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Ooh, good point! In my mind, 0 is not a number, as, a number is a representation of a quantity and "nothing" is not a quantity. Zero is a placeholder though, useful in numeric representation systems that use columns.
In that case, 0 also represents the "first" value, even though it doesn't amount too much. (Ever hear the trick statement, i know the score before a baseball game starts? It is 0 to 0.) Hence, the poll question is really, what is the first representational digit in base 1, colloquially asked as "what is the first number after 0".
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In my mind, 0 is not a number, as, a number is a representation of a quantity and "nothing" is not a quantity.
I'm intrigued. Can you elaborate on that? In what sense is zero not a quantity?
Related question: would you consider the empty set a set? And if so: would you say that it makes sense to talk about the cardinality of a set, i.e. the number of its elements? And what would the cardinality of the empty set be?
Ever hear the trick statement, i know the score before a baseball game starts? It is 0 to 0.
I think it'd be more accurate to say that it's NULL to NULL, to borrow a term from databases  though NULL is itself a rather overloaded concept that represents (and, arguably, conflates) many distinct concepts at once.
Hence, the poll question is really, what is the first representational digit in base 1, colloquially asked as "what is the first number after 0".
In that case, I'm tempted to answer "an ε that's smaller than any real number>0", but I'll leave that to people who actually know a bit about nonstandard analysis (I don't!). ;)
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Re: In base 1, the number after 0 is:
by duelafn (Parson) on May 01, 2014 at 10:58 UTC

0
00
000
0000
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The only sane answer. Thanks,
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Re: In base 1, the number after 0 is:
by zentara (Archbishop) on May 01, 2014 at 13:59 UTC

∞ of course. :) My thought is this: In order to maintain balance in the universe, 0 must have an appropriate counter number, otherwise 0 would become a singularity! So ∞ has the appropriate characteristics, to counteract the infinite smallness of 0. You could look at it like 0 with a twist. Maybe it's a ALIVE, pulsating between it's 0 and twisted ∞state. :)
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Re: In base 1, the number after 0 is:
by ww (Archbishop) on May 01, 2014 at 11:58 UTC

Why, 42 of course
check Ln42!
Quis custodiet ipsos custodes. Juvenal, Satires
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chacham:
I usually use * or B, depending on context....
...roboticus
When your only tool is a hammer, all problems look like your thumb.
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Re: In base 1, the number after 0 is:
by kcott (Bishop) on May 01, 2014 at 17:28 UTC

A Thumb!
I checked it: zero was a fist; 1_{10} was a thumb; 2_{10} was a thumb and forefinger; ...
Unfortunately, the options:

Thumb

Other

None of the above
were all missing, so I wasn't able to vote in this poll. :(
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Deaf people have improved this slightly :)
They consider a hand with only the thumb extended to mean "6", while the index finger means "1". Zero is signed by forming a round shape using the thumb and index finger. This way they can sign the numbers 0 .. 9 using one hand only.
 FloydATC
Time flies when you don't know what you're doing
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How do they do 5? Did you mean 5 when you typed 6?
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Well, OK. But I think 0 looks more like roboticus' thumb than mine. :)
Just to explain that quip, ...
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Re: In base 1, the number after 0 is:
by davido (Cardinal) on May 01, 2014 at 23:02 UTC

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Re: In base 1, the number after 0 is:
by wjw (Priest) on May 01, 2014 at 19:03 UTC

Interesting exercise in mental gymnastics... .
In base 1 there is no symbol for 0(zero) if one is to believe Wikipedia. Thus there is no character after the character 0(zero) because that character does not exist in that system. So counter to my incorrect and uninformed vote, the better answer is probably 'heresy'. One learns the strangest things here... . Yet it does leave one open to asking what nothing is in a system which has no representation for it.
Perhaps if one is stuck in an unary system, zero would be thought of as a quality instead of as a quantity. I think I like that...
...the majority is always wrong, and always the last to know about it...Insanity: Doing the same thing over and over again and expecting different results...
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base 2 uses 0 and 1 as its digits
base 10 uses 0,1,2,3,4,5,6,7,8,9
base n uses 0 .. n1 as it's list of digits where n is the number of digits avaliable
since in the case of base 1 n1 would be 11 or 0 the entire list of digits would be 0..0. Making the answer 00 or in common base 10 "2".
If we consider that English speaking non programmers who treat 0 and null as the same value we can infer that the choice to use 0 as the entire list of digits in base 1 is flawed as general consensus would be to use 1 as the entire list of digits available in base 1. In this case the number after 0, which is effectively null, would be 1.
my $foo = null;
$foo ++;
print $foo;
#1
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I agreee with you that the number after 0 is 00 in base 1, but I'd say it is 0 in base 10.
Also I'd write your code as:
my $n = ''.0;
$n++;
print "$n\n";
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Re: In base 1, the number after 0 is:
by mr_mischief (Monsignor) on May 06, 2014 at 14:09 UTC

If there is a 0 in your base 1, then it is the only symbol. The question sort of asks the reader to assume it is part of the sequence. The next number would be 00.
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Re: In base 1, the number after 0 is:
by thezip (Vicar) on May 05, 2014 at 22:59 UTC

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Re: In base 1, the number after 0 is:
by chacham (Prior) on May 01, 2014 at 19:08 UTC

The idea of ℵ₀ (alephzero), and for that matter, "many", comes from George_Gamow's book, One_Two_Three_..._Infinity. He explains that in one language there are words for "one", "two", "three", and after that, "many", because it didn't matter at that point. (a search for one two three many found this which mentions this idea.)
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In terms of database design, class design, and many other programming tasks, it is often useful to restrict your concept of numbers to there being only three numbers:
For example: never design a database that can store two email addresses for a contact. It should store none, one, or many. Now, your interface might restrict people to entering a "sensible" number of email addresses like two, or six, or ten, but the database design should stick with none, one, or many.
use Moops; class Cow :rw { has name => (default => 'Ermintrude') }; say Cow>new>name
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In terms of database design, class design, and many other programming tasks, it is often useful to restrict your concept of numbers to there being only three numbers
That is a good rule of thumb, but it is just a starting point. The real rule is, in my mind, whether a data rule requires it; and if it does, how many. If how many cannot be answered with a specific number, a new (child) table is used for them. Otherwise, same table.
For example, if storing email addresses and one alternate, it may make sense to store both email addresses in the same table. Another example (from my current project), if you have an entity created with up to 12 parts (each part being similar to a level), it is likely better to store the 12 parts in the same table.
Technicalities, perhaps. But, this is what i do for a living.
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Re: In base 1, the number after 0 is:
by Discipulus (Abbot) on May 06, 2014 at 07:50 UTC

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Re: In base 1, the number after 0 is:
by psini (Deacon) on May 06, 2014 at 13:57 UTC

Any sequence of digits matching /^0*10*$/ evaluates to "one" in base 1.
Rule One: "Do not act incautiously when confronting a little bald wrinkly smiling man."
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Re: In base 1, the number after 0 is:
by blue_cowdawg (Monsignor) on May 15, 2014 at 15:45 UTC

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Re: In base 1, the number after 0 is:
by chacham (Prior) on May 01, 2014 at 12:26 UTC

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$ perl Mopen=OUT,:utf8,:std E '
say "\N{SATURN} ", chr 0x2644;
'
♄ ♄
Chart with other astrological symbols: [Note: PDF link] http://www.unicode.org/charts/PDF/U2600.pdf
++ [delayed until Vote Fairy next visits] for link to that excellent obfuscation. :)
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Re: In base 1, the number after 0 is:
by lenieto3 (Acolyte) on May 20, 2014 at 11:24 UTC

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Re: In base 1, the number after 0 is:
by taint (Chaplain) on May 23, 2014 at 15:39 UTC

Why was ON not listed a potential candidates?
In machine language, the binary (base 1) counting system is used as ON. For example; if a latch is open, it's OFF. The same could be said, where processors (CPU's) are concerned. In fact, a CPU is not unlike a light switch. In the same way that the speed by which you can turn the light(s) on, and off, is the frequency of that cycle. So it is with the CPU  the Frequency is determined by how fast the CPU cycles. So in essence; the CPU is no more than a light switch. So it is, where the binary/base1 numbering/counting system is.
In conclusion; it is my assertion that the correct answer would have been "none of the above". As a result, I couldn't vote.
Chris
¡λɐp ʇɑəɹ⅁ ɐ əʌɐɥ puɐ ʻꜱdləɥ ꜱᴉɥʇ ədoH
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Re: In base 1, the number after 0 is:
by SueHai (Initiate) on May 21, 2014 at 09:30 UTC

first: a great "system"
hello monks,
4 me the number "0" is not definined, cause u r not able to execute a division.
dividing by "0" is not defined > a rule in the mathematic
a logic and human view would say to me the "0" after "1" is "10" > an easy and real annoying view(based on in germany calles "idiottests".
have a lot of fun ;)  [reply] 