5 ms·

Base 1 does make sense! 0 = 0 00 = 1 000 = 2 0000 = 3 etc

by xyproto 14y ago

eggnet 14y ago
What you've done is define your own number system, I do not believe you are representing what "base 1" might be. If a base means, you can write numbers of this form: abc Where the value is: aB^2 + bB^1 + cB^0 and you can only have B symbols, then your one symbol for base 1 would need to be 1, still useless, but not completely: 1 = 11^0 = 1 11 = 11^1 + 11^0 = 2 ... Note that you cannot represent 0 in base 1 with this method. If you choose 0 as your one symbol for base 1, then the only number you can represent is 0. I assert this is even more useless than selecting 1 as the symbol. 0 = 01^0 = 0 00 = 01^1 + 01^0 = 0 ... As far as I can tell, the example was trying to interpret "10" as base 1. 10 has two different symbols which truly does not make sense in base 1. I assert that base 1 is not a valid base, because you cannot represent all integers in it. Additionally, the "unary point" or whatever it would be called, would serve no purpose: 1.1 = 11^0 + 1*1^-1 = 2 I'm not sure how that might disqualify something for a "base" but it certainly doesn't help :) Probably the strongest argument is the inability to represent 0.
- ced 14y ago
  I had the same reaction as you had, but apparently, OP is correct: https://en.wikipedia.org/wiki/Base_1 https://en.wikipedia.org/wiki/Base_1 though you are right that it's not the same as base N, N>1. Also, Wikipedia uses |||| to represent 4 instead of 0000. It makes more sense.
- ehsanu1 14y ago
  You can represent 0 by absence. : 0 o : 1 oo : 2 ooo: 3 Of course, this is not a practical notation, since 0 would hard to distinguish from actual absence, but it would be viable in some situations: a table of numbers say, where you know that no cells are empty. So theoretically, it is possible to represent 0 in base 1, regardless of its obvious impracticalities.
NegativeK 14y ago
That's using a different notation than our more familiar number systems, though. If we were treating it like base 2 (or 10 or 8 or 16), we would evaluate 0000 as 1^30+1^20+1^10+1^00 = 0. A number system where the only number you can represent is 0 is a bit less useful.
deleted 14y ago
[deleted]

Base 1 does make sense! 0 = 0 00 = 1 000 = 2 0000 = 3 etc

by xyproto 14y ago

Base 1 does make sense! 0 = 0 00 = 1 000 = 2 0000 = 3 etc

What you've done is define your own number system, I do not believe you are representing what "base 1" might be. If a base means, you can write numbers of this form: abc Where the value is: aB^2 + bB^1 + cB^0 and you can only have B symbols, then your one symbol for base 1 would need to be 1, still useless, but not completely: 1 = 11^0 = 1 11 = 11^1 + 11^0 = 2 ... Note that you cannot represent 0 in base 1 with this method. If you choose 0 as your one symbol for base 1, then the only number you can represent is 0. I assert this is even more useless than selecting 1 as the symbol. 0 = 01^0 = 0 00 = 01^1 + 01^0 = 0 ... As far as I can tell, the example was trying to interpret "10" as base 1. 10 has two different symbols which truly does not make sense in base 1. I assert that base 1 is not a valid base, because you cannot represent all integers in it. Additionally, the "unary point" or whatever it would be called, would serve no purpose: 1.1 = 11^0 + 1*1^-1 = 2 I'm not sure how that might disqualify something for a "base" but it certainly doesn't help :) Probably the strongest argument is the inability to represent 0.

ced 14y ago
I had the same reaction as you had, but apparently, OP is correct: https://en.wikipedia.org/wiki/Base_1 https://en.wikipedia.org/wiki/Base_1 though you are right that it's not the same as base N, N>1. Also, Wikipedia uses |||| to represent 4 instead of 0000. It makes more sense.
ehsanu1 14y ago
You can represent 0 by absence. : 0 o : 1 oo : 2 ooo: 3 Of course, this is not a practical notation, since 0 would hard to distinguish from actual absence, but it would be viable in some situations: a table of numbers say, where you know that no cells are empty. So theoretically, it is possible to represent 0 in base 1, regardless of its obvious impracticalities.

NegativeK 14y ago

That's using a different notation than our more familiar number systems, though. If we were treating it like base 2 (or 10 or 8 or 16), we would evaluate 0000 as 1^30+1^20+1^10+1^00 = 0. A number system where the only number you can represent is 0 is a bit less useful.

deleted 14y ago

[deleted]