What's a number?
- Thread starter Souron
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PeteAtoms
FormulaRandom
It's a symbol (visually and mentally) that represents quantity or magnitude.
Useful to distinguish varying degrees of 'more' and 'less.'
Useful to distinguish varying degrees of 'more' and 'less.'
So I'm asking about the thing it stands for, not the numeral itself.
You say a number is a quantity or a magnitude. What are those, and are they different?
Formaldehyde
Both Fair And Balanced
Numbers can be very confusing. But most people seem to agree that one is the loneliest number that you'll ever do.
Link to video.
Link to video.
ParkCungHee
Deity
- Joined
- Aug 13, 2006
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- 12,921
Some however, contend that two can be as sad as one.
PeteAtoms
FormulaRandom
I didn't say number were quantity or magnitude, they just represent those ideas.
Quantity and magnitude are measurements describing the physical universe and relationships between mass/energy within space. If you have two 'things,' a relationship exists between them and with the observer as well.
If you have more apples than me, you would need a way to communicate how much more.
NUMERICAL COGNITION
Onionsoilder
Reaver
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Quantity is an amount of something. Like 7 apples. There are 7 separate, distinct apples.
Magnitude is more of a scale, I believe. Like a magnitude 3 earthquake. It's not three separate earthquakes, but one larger one.
So all numbers are a ratio?
You'll be happy to know that this forum has [wiki][/wiki] tags.
At a high level they are a "convention", an agreed upon way of organizing things. In the beginning they were for counting and measuring.
Perfection
The Great Head.
Numbers have all sorts of amazing properties.
For instance:
There's one number that if you use on a telephone lets you speak to Perf! Many people have resorted to desperate measures in attempt to figure out what this number is.
For instance:
There's one number that if you use on a telephone lets you speak to Perf! Many people have resorted to desperate measures in attempt to figure out what this number is.
Numerals are conventions. But numbers, like all things in math, exist whether there is anyone around to use them or not. Right?
azzaman333
meh
Numbers are fun.
God made the natural numbers, all the rest is the work of man.
- Leonard Kronecker
More concrete answer: http://en.wikipedia.org/wiki/Peano_axioms
edit: also relevant quote
Numbers exist only in our minds. There is no physical entity that is number 1. If there were, 1 would be in a place of honor in some great museum of science, and past it would file a steady stream of mathematicians gazing at 1 in wonder and awe.
- Linear Algebra by Fraleigh/Beauregard
- Leonard Kronecker
More concrete answer: http://en.wikipedia.org/wiki/Peano_axioms
edit: also relevant quote
Numbers exist only in our minds. There is no physical entity that is number 1. If there were, 1 would be in a place of honor in some great museum of science, and past it would file a steady stream of mathematicians gazing at 1 in wonder and awe.
- Linear Algebra by Fraleigh/Beauregard
No they're not.
ParadigmShifter
Random Nonsense Generator
Peano is a good place to start.
I'd say a number is any finite quantity though. Then we can say i = sqrt(-1) is a number too
Then you can start classifying what properties your numbers satisfy.
I'd say a number is any finite quantity though. Then we can say i = sqrt(-1) is a number too
Then you can start classifying what properties your numbers satisfy.
As Pete Atoms points out numbers are closely related to quantity and magnitude, which are physical properties, though not the kind of entities you can put in a museum.
Also, the Peano axioms are only about natural numbers. How do you define the set of real numbers as an operation on the natural numbers?
ParadigmShifter
Random Nonsense Generator
Numerals and nomenclature certainly are conventions. I'm not sure how you define numbers (assigned values?), so I'll hold off a bit on that part. Now "all things math" are relationships between assigned values. Math is an agreed upon language that expresses a relationship so we can understand/use that relationship. I would say that the relationships do exists independent of any expression we make of them. Birds fly all by themselves; they do not need nor do their brains use any mathematics to do so. Math is our way of expressing natural events. math does not exist out side of our brains.
