Is 0 A Positive Integer? Watch

HowToBeABlobfish
Badges: 18
Rep:
?
#1
Report Thread starter 2 days ago
#1
Alright so basically the question refers to "distinct positive integers", does 0 count as a positive integer?
0
quote
reply
LeapingLucy
  • Community Assistant
Badges: 19
Rep:
?
#2
Report 2 days ago
#2
No, it's neither positive nor negative.
1
quote
reply
DFranklin
Badges: 18
Rep:
?
#3
Report 2 days ago
#3
(Original post by HowToBeABlobfish)
Alright so basically the question refers to "distinct positive integers", does 0 count as a positive integer?
There isn't a totally clear consensus, so it can depend on context. In the UK, I think it's more common to say 0 is NOT a positive integer than to say it is.

When I was at Cambridge, the consensus seemed to be that 0 was NOT positive and also 0 \notin \mathbb{N}. But then we also had the slightly contradictary decision that 0 \in \mathbb{Z}^+; explictly, that \mathbb{Z}^+ refered to the set of non-negative integers, not the set of positive integers.
1
quote
reply
HowToBeABlobfish
Badges: 18
Rep:
?
#4
Report Thread starter 2 days ago
#4
(Original post by DFranklin)
There isn't a totally clear consensus, so it can depend on context. In the UK, I think it's more common to say 0 is NOT a positive integer than to say it is.

When I was at Cambridge, the consensus seemed to be that 0 was NOT positive and also 0 \notin \mathbb{N}. But then we also had the slightly contradictary decision that 0 \in \mathbb{Z}^+; explictly, that \mathbb{Z}^+ refered to the set of non-negative integers, not the set of positive integers.
Sozzles do you think you can please translate the 2nd paragraph?
0
quote
reply
DFranklin
Badges: 18
Rep:
?
#5
Report 2 days ago
#5
(Original post by HowToBeABlobfish)
Sozzles do you think you can please translate the 2nd paragraph?
\mathbb{N} are the Natural numbers; again, people will argue whether the natural numbers start with 0 (i.e. 0, 1, 2, 3, ...) or 1 (1, 2, 3, ...), but the consensus at Cambridge was that they did NOT include 0.

But in that case you often want a way of denoting the set {0, 1, 2, 3, ... }; again at Cambridge this was denoted by \mathbb{Z}^+. Looking at this, you'd think it was "the set of positive integers", but in fact it was considered to be "the set of non-negative integers".

[To close the circle, people who say that \mathbb{N} = \{0, 1, 2, 3, ... \} will generally also say that \mathbb{Z}^+ = \{1, 2, 3, ... \}].
0
quote
reply
anosmianAcrimony
Badges: 20
Rep:
?
#6
Report 2 days ago
#6
In the U.S., I was taught that the natural numbers were 1, 2, 3, ..., that the whole numbers were 0, 1, 2, 3, ..., and that the integers were 0, plus or minus 1, plus or minus 2, ...

So 0 is a whole number and an integer, but not a natural number, and it's neither positive nor negative.
0
quote
reply
DFranklin
Badges: 18
Rep:
?
#7
Report 2 days ago
#7
(Original post by anosmianAcrimony)
In the U.S., I was taught that the natural numbers were 1, 2, 3, ..., that the whole numbers were 0, 1, 2, 3, ..., and that the integers were 0, plus or minus 1, plus or minus 2, ...

So 0 is a whole number and an integer, but not a natural number, and it's neither positive nor negative.
Those are my personal conventions, but I have definitely seen people (including authors and lecturers) who disagree - although it's possible the conventions have solidified in the 30odd years since I was an undergrad.
0
quote
reply
X

Reply to thread

Attached files
Write a reply...
Reply
new posts
Latest
My Feed

See more of what you like on
The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

Personalise

University open days

  • University of Lincoln
    Brayford Campus Undergraduate
    Wed, 12 Dec '18
  • Bournemouth University
    Midwifery Open Day at Portsmouth Campus Undergraduate
    Wed, 12 Dec '18
  • Buckinghamshire New University
    All undergraduate Undergraduate
    Wed, 12 Dec '18

Do you like exams?

Yes (137)
18.51%
No (449)
60.68%
Not really bothered about them (154)
20.81%

Watched Threads

View All