How come zero and one are so important to our number system?

In summary, the conversation discusses the significance of the numbers 0 and 1 in our number system, as they have unique properties such as being additive and multiplicative identities and having special properties in different number systems. The conversation also touches on the concept of identities in mathematical structures and how 0 and 1 are still considered identities in other systems, but not necessarily the "same thing". The conversation ends with a mention of how 0 and 1 also have complementary concepts in multiplication and addition.
  • #1
Gale
684
2
How come zero and onw are so important to our number system? they both have oddities about them that are particular only to them... identy properties, division by zero... and whatnot. Is this because we're in a base 10 system? in say binary... are there special numbers like that? or in a base 12 system?

...should this be in number theory?
 
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  • #2
Well, something has to be the additive and multiplicative identities. :smile:

Ok, that's not entirely true; not all mathematical structures have to have such identities... but identities are very useful things, and pretty much all of the important algebraic structures have them.



Also, binary, decimal, and base-12 (duodecimal, I think) numbers are all the same numbers... these are just different systems of writing them.
 
  • #3
soo... one and zero retain their identitive properties even in other number systems... i suppose that made sense... same numbers... i guess there's no way to get different numbers... but hmm... how about like... i dunno... i have to think some more...
 
  • #4
Well, binary, hexadecimal, et cetera are all the same numbers, so 0 and 1 are the same thing in all of them. (They're all written the same way too, of course).


But in other things, such as abstract groups, fields, and vector spaces, we still call the additive and multiplicative identities 0 and 1, but it would be misleading to say they're the "same thing".
 
  • #5
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1. Why do we use zero in our number system?

In our number system, zero is used as a placeholder to indicate the absence of a value in a specific place. This allows us to represent larger numbers and perform mathematical operations more efficiently. Without zero, our number system would not be as versatile and would limit our ability to represent and manipulate numbers.

2. What makes one so important in our number system?

One is important in our number system because it is the foundation of counting and representing individual units. It is also the basis for all other numbers, as every number can be broken down into multiples of one. Additionally, one is used as a reference point for fractions and decimals, allowing us to express numbers in different forms.

3. How did the concept of zero and one develop in our number system?

The concept of zero and one in our number system has evolved over time and has been influenced by various cultures and civilizations. The ancient Egyptians used a symbol for zero as a placeholder, while the ancient Greeks saw zero as a concept but did not have a symbol for it. The concept of one as a single unit has been present since early human civilizations and has been refined and standardized through various mathematical developments.

4. Can our number system function without zero and one?

No, our number system cannot function without zero and one. These two numbers are essential for representing and manipulating numbers. Without zero, we would not be able to represent larger numbers efficiently, and without one, we would not have a foundation for counting and representing individual units.

5. Are zero and one important in other fields besides mathematics?

Yes, zero and one have significance in many fields besides mathematics. In computer science, binary code uses only zero and one to represent data and instructions. In philosophy and logic, zero and one are used to represent true and false, respectively. In everyday life, we use zero and one in various symbols and codes, such as the power button (zero) and the checkmark (one).

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