Is this a correct way to describe number sets?

  • #26
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Please don't!
And they shouldn't. ##0## is a human achievement and nothing natural. :cool:
I also agree to this viewpoint
 
  • #27
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But sure, ##0## is unnatural. I have 2 apples and give 2 apples to my brother. What I have left is nothing natural??

Also, axiomatic set theory is pretty clear on the issue that ##0## should be a natural number. You'd make a mess out of the theory otherwise.
 
  • #28
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You think Graham's number is natural?
Hmm, I'd rather say funny. In any case it's a nice example how to code something huge in a small number of digits.
 
  • #29
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Did we invent the numbers? or discover them?
 
  • #30
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Did we invent the numbers? or discover them?
Meh, once you rigorously define those terms, we might find an answer. So far, nobody has really given a satisfactory definition.
 
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  • #31
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But sure, ##0## is unnatural. I have 2 apples and give 2 apples to my brother. What I have left is nothing natural??

Also, axiomatic set theory is pretty clear on the issue that ##0## should be a natural number. You'd make a mess out of the theory otherwise.
But this argument is essentially practicability as it is to exclude units to be prime. I have no problem when people work with ##\mathbb{N}_0## though.
 
  • #32
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Meh, once you rigorously define those terms, we might find an answer. So far, nobody has really given a satisfactory definition.
ok boss..this is all way over my head. xD
 
  • #33
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But this argument is essentially practicability as it is to exclude units to be prime. I have no problem when people work with ##\mathbb{N}_0## though.
Well, clearly you don't think math should be elegant. I think elegance trumps everything else. And if you believe in elegance, ##0## should be a natural.
 
  • #34
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number is undefined, so is point, proposition, true, false, set, element...o0):frown:
 
  • #35
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Well, clearly you don't think math should be elegant. I think elegance trumps everything else. And if you believe in elegance, ##0## should be a natural.
Oh no. I won't turn into this ... Far too obvious!
 
  • #36
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Compromise:

natural.png


Include 0 only half. Is that natural enough?
 
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  • #37
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Compromise:

View attachment 106007

Include 0 only half. Is that natural enough?
We have to ask the Indians. As far as I know they have the copyright on the ##0##. I'm sure we've had numbers when we lived in Africa, but it took a civilization to use the ##0##. Probably some bookies ....
 
  • #38
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We have to ask the Indians. As far as I know they have the copyright on the ##0##. I'm sure we've had numbers when we lived in Africa, but it took a civilization to use the ##0##. Probably some bookies ....
Some tribes count as ##1,2,3,\text{many}##. So I deny that the number ##10## is very natural.
 
  • #39
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Some tribes count as ##1,2,3,\text{many}##. So I deny that the number ##10## is very natural.
It's just another name for 2. :wink:
 
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