Current Events > Is 0 a natural number?

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teepan95
06/16/20 1:18:37 AM
#1:


Does the set of natural numbers (without further qualification) include zero?


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ZMythos
06/16/20 1:19:07 AM
#2:


It depends on who you ask.

Most often no, the naturals start with one.

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pepper2012
06/16/20 1:20:42 AM
#3:


Yes

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TreyFlowers
06/16/20 1:20:58 AM
#4:


0 is the absence of a number

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MedeaLysistrata
06/16/20 1:24:21 AM
#5:


natural numbers
noun
  1. the positive integers (whole numbers) 1, 2, 3, etc., and sometimes zero as well.
Why is it sometimes? Is this like y being a vowel?

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teepan95
06/16/20 1:25:44 AM
#6:


TreyFlowers posted...
0 is the absence of a number

Nah, it's the neutral element of addition. But it is an element and therefore a number :P
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ZMythos
06/16/20 2:08:26 AM
#7:


MedeaLysistrata posted...
Why is it sometimes? Is this like y being a vowel?
Actually yes.

We often denote N as the natural numbers including zero

and N^+ as the strictly positive natural numbers.

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MabusIncarnate
06/16/20 2:09:08 AM
#8:


One is the loneliest number

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Naysaspace
06/16/20 2:10:31 AM
#9:


No.

Natural numbers:
1,2,3,....
Whole numbers:
0,1,2,3...
Integers
-2, -1, 0, 1, 2, ....
Rational Numbers
1/2, 3/4, 4/5, etc...
Irrational numbers:
Pi, e, sqrt(2), etc....
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MabusIncarnate
06/16/20 2:11:43 AM
#10:


Naysaspace posted...
No.

Natural numbers:
1,2,3,....
Whole numbers:
0,1,2,3...
Integers
-2, -1, 0, 1, 2, ....
Rational Numbers
1/2, 3/4, 4/5, etc...
Irrational numbers:
Pi, e, sqrt(2), etc....
Ohh look at calculator mcmath pants over here.

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teepan95
06/16/20 2:31:24 AM
#11:


Naysaspace posted...
Whole numbers:
0,1,2,3...

disgusting
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TreyFlowers
06/16/20 2:34:25 AM
#12:


Naysaspace posted...
sqrt(2)

Squirtle is a Pokemon not a number

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Eevee-Trainer
06/16/20 2:38:57 AM
#13:


It's ultimately a matter of opinion, but I say yes just so my naturals can be an additive monoid.

At the end of the day I don't really care though so long as you're clear and your notation is unambiguous.

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