Why is the number 1 a natural number?

[Fredrick]

I am wondering if anyone can give me a clear answer on what to do with the number 1, and if my thinking about the number 1 is correct.

The number 1 is included in the definition of the natural numbers, and I am wondering what that 1 represents. 1 is known as 'unity,' but it is also seen as singular. I have never seen a unity that is singular.

Does anyone have an example of a singular unity? I know that a nation for instance can display unity, but the situation is here that the nation has been created from multiple members. Naturally, there are units (apples, oranges) that can be brought back to 1, but those 1s are part of a larger picture too. Can anyone think of an example in which unity is not plural? Is the singular just an abstract?

 

[matt grime]

That's not the mathematical meaning of unity (your example of a nation I mean), nor does the use of unit to describe 1 mean it is a unit in the sense of metre/apple/orange/second.

Units are elements in a ring that invertible (are divisors of the identity element).
Unity and oneness might be the synonym you're searching for.

 

[HallsofIvy]

"1" is very well defined in mathematics (in fact, it may have many different definitions in different situations) but none of the examples you give are mathematical situations- they are all applications of mathematics where the definitions depend upon the particular application.

 

[Fredrick]

Still wondering

Thank you for both your answers. They do contain good information that I find usable, but is it possible for either one of you to come up with an example I can sink my teeth in? Unity and oneness does not do the trick. Am I getting the drift correctly that 1 is used mainly in the abstract?

 

[matt grime]

1 denotes the multiplicative identity in a ring, mathematically speaking that's as complicated as it gets. Any issue other than that is down to your personal philosophy of how to apply mathematics. When a mathematician refers to unity as in "these two quantities differ by unity" they mean x-y=1, where 1 is the multiplicative identity of the ring in question.

The use of unity you are thinking of is not mathematical, and mathematics says nothing about that, nor does it even try.

1 is defined as the object in such that 1*x=x for all x (in the relevant ring, say), nothing to do with counting oranges.

And I can't decide what "brought back to 1" means

 

[Math Is Hard]

Does anyone have an example of a singular unity? I know that a nation for instance can display unity, but the situation is here that the nation has been created from multiple members. Naturally, there are units (apples, oranges) that can be brought back to 1, but those 1s are part of a larger picture too. Can anyone think of an example in which unity is not plural? Is the singular just an abstract?

Are you searching for an example of a natural object that is indivisible?

 

[Fredrick]

The picture is getting clearer. Thanks.

I think the picture is getting clearer, Matt, and I want to thank you for your help. Reading your words, 1 is a number that exists in combinations as the possible multiplicative identity of a ring. Otherwise the 'nature' of 1 is more elusive - personal - depending on what the particular math is used for.

Math is Hard, could you give me an example of a natural object that is indivisible?

 

[Math Is Hard]

Math is Hard, could you give me an example of a natural object that is indivisible?

Outside of my Aunt Paula's home-made sourdough dinner rolls, no. You can't even cut those things with diamonds.

People who understand the sub-atomic realms (which I don't) might have a better answer to this.

 

[mathwonk]

...one nation, indivisible, with liberty and justice...

 

[Fredrick]

Thank you

I guess I should thank you all for the enlightment.

Mathwonk, wouldn't it be wonderful if your words were really true. Or were you talking about the country I orginate from?