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Current time: May 24, 2022, 11:39 am

Poll: Is zero a natural number?
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Yes
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No
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Total 4 vote(s) 100%
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Is zero a natural number?
#11
RE: Is zero a natural number?
"Zero f given". Its natural.
[Image: keep-calm-and-praise-the-sun.jpg]
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#12
RE: Is zero a natural number?


[Image: Fenrir-sign.jpg]
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#13
RE: Is zero a natural number?
(January 18, 2022 at 10:40 am)Ranjr Wrote: Sometimes nothing is a real cool hand.

Kick a buck.

Boru
‘Let me never fall into the vulgar mistake of dreaming that I am persecuted whenever I am contradicted.’ Ralph Waldo Emerson
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#14
RE: Is zero a natural number?
42, and 68, the only numbers nature cares about.
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#15
RE: Is zero a natural number?
(January 18, 2022 at 11:11 am)no one Wrote: 42, and 68, the only numbers nature cares about.

69?
And without delay Peter went quickly out of the synagogue (assembly) and went unto the house of Marcellus, where Simon lodged: and much people followed him...And Peter turned unto the people that followed him and said: Ye shall now see a great and marvellous wonder. And Peter seeing a great dog bound with a strong chain, went to him and loosed him, and when he was loosed the dog received a man's voice and said unto Peter: What dost thou bid me to do, thou servant of the unspeakable and living God? Peter said unto him: Go in and say unto Simon in the midst of his company: Peter saith unto thee, Come forth abroad, for thy sake am I come to Rome, thou wicked one and deceiver of simple souls. And immediately the dog ran and entered in, and rushed into the midst of them that were with Simon, and lifted up his forefeet and in a loud voice said: Thou Simon, Peter the servant of Christ who standeth at the door saith unto thee: Come forth abroad, for thy sake am I come to Rome, thou most wicked one and deceiver of simple souls. And when Simon heard it, and beheld the incredible sight, he lost the words wherewith he was deceiving them that stood by, and all of them were amazed. (The Acts of Peter, 9)
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#16
RE: Is zero a natural number?
Computer scientists and set theorists start counting at 0. Most other people start counting at 1.

But, in set theory, 0 is a natural number and is identified with the empty set, just like 1 is identified with the set containing just the empty set.
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#17
RE: Is zero a natural number?
Here's another expert weighing in:

[Image: Count-zero.jpg]
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#18
RE: Is zero a natural number?
[Image: icon_quote.jpg]this guy:
42, and 68, the only numbers nature cares about.

[Image: icon_quote.jpg]Jehanne:
69?


No, 68.


You do me, and I owe you one. [Image: Gagged.png]
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#19
RE: Is zero a natural number?
If zero is not 'natural', where does than leave negative numbers?

Yeah Poly, I'm looking to you to hurt my math brain again.
I don't have an anger problem, I have an idiot problem




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#20
RE: Is zero a natural number?
(January 18, 2022 at 5:45 pm)brewer Wrote: If zero is not 'natural', where does than leave negative numbers?

Yeah Poly, I'm looking to you to hurt my math brain again.

The usual progression is something like this:

1. Natural numbers: 0,1,2,3,4,....

2. Integers: Either a natural number or the negative of a natural number, so ..,-3, -2, -1, 0, 1, 2, 3,...

3. Rational numbers: Fractions, one integer divided by a non-zero integer. 2/3, -5/8, 13/2, 4=4/1, -123/43,....

4. Real numbers: intuitively, numbers with (possibly infinite) decimal expansions. pi, e, sqrt(2), ....

5. Complex numbers. If i is the square root of -1, then a complex number is one of the form a+bi where a and b are real numbers.

These are the basic number systems, but there are a host of others.

Algebraic numbers: those that are roots of some polynomial with integer coefficients. sqrt(2) is algebraic. so is sqrt(2)+cbrt(5).

Gaussian integers: those complex numbers a+bi where a and b are integers. these have many properties in common with the integers.

These are the usual algebraic number systems.

But we can go in a different direction. All natural numbers are also 'cardinal numbers': these count the 'number of things' in sets. The natural numbers are, specifically, the
*finite* cardinal numbers.

But there are infinite cardinal numbers as well. These are studied in set theory and usually not as algebraic structures because they lack many of the 'nice' properties of the other systems above. if you are trying to say infinity is a number, this is what you are probably talking about.

Ordinal numbers: instead of the 'size' of a set, we put an 'order structure' on the set and compare different order structures. Usually, we do this with order structures that are 'nice' in the sense of being 'well-ordered' (a technical term that I can go into if anyone wants). The natural numbers are, again, the finite ordinal numbers. But ordinal numbers have a much more complex structure than cardinal numbers do. They also fail to obey certain fairly natural algebraic properties, so are usually studied by set theorists as well.

In standard set theory, following Von Neumann, every cardinal number is an ordinal number, but not vice versa.
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