Zero doesn’t represent nothing, it represents a non countable quantity for the base being used.
In other words, you do not have nothing and Jim has 5 apples, you have less than the minimum countable number of apples and Jim has 5 apples. It’s abstract. Saying “I do not have any cake” is the same as saying you have 0 cake in concept. Linguistically we use different phrasing when discussing the non quantifiable but math is a different language. Importantly- math has ways to differentiate that which is unquantifiable because it is not observable- 0 apples, I do not observe you having any apples. Non quantifiable because it is two small to express but is present or observable, non quantifiable because it is too large or it’s magnitude is not observable but is present etc.
critically thought, “0” must apply to something. It can’t exist on its own. An example is zero apples- zero applies to apples, if you had nothing you’d be naked and skinless and boneless and nonexistent-
You have something, or many things, we just cannot observe and have no evidence of the presence of a specific thing- in this case apples. It does not mean you never had it will ever have any apples, it only applies to the exact moment and/or circumstances being referenced.
“When you turn on a calculator it says zero- so zero is existing alone- check mate!”
Not so fast dear friend. That is zero the place holder and it never exists alone. Blank would imply nothing. A zero is there to represent that you have zero of a specific thing. In this case you have zero ones in your ones column. Place a decimal and you have 0 ones or 0 tenths and so on. We don’t always show zero and that blank doesn’t exactly represent nothing. Technically we could write “100” as “00100.0000000” or “0000000000000000000000000000000000000000000000000000000100.0000000000000000000000000” or we could put a billion or a googolplex or “infinite” zeros and never finish writing a single number.
Asides being hard to read there is a lot of space taken up for no reason there. There are “infinite” places to the left of hundreds, thousands and tens thousands and hundred thousands and millions on to billions and on and on, and the same is true of decimal places. When we have a while number we rarely need to express that the decimal value is “0” because omitting those places implies it and there isn’t any relevant information there. We don’t need to hold the places forward of the highest value representing existence of physical data.
There are exceptions to this but zero as a place holder exists as a convenience to fill relevant data fields primarily for formatting and parsing.
This is a big factor in the “cannot divide by zero” convention. Zero doesn’t strictly exist. It holds the conceptual place of something that doesn’t exist. The concept is firmly expressed to anyone with passing familiarity with algebra but it’s actually quite intuitive. If we compare numbers we must have numbers to compare- or some concept to represent a number.
“Balance the equation.” This isn’t some silt rule, it’s a matter of perception and reality.
If you and I want to compare test grades, if I say I received an A, I need to know what you got to compare. If you didn’t complete the test the comparison would be an A to a did not complete. Numerically a 97 to a 0 on a points scale. This is different than if we do not know what you got- we could say 97 to X in this case or express it in writing as “97 to ?”
But as you say you can’t “have nothing” right? As far as we know, nothing doesn’t exist or we can’t conceptualize it. So where you have A and B and are comparing values, A must have a value and B must have a value. The value can be unknown or unquantifiable but there must be SOME value.
In other words, you do not have nothing and Jim has 5 apples, you have less than the minimum countable number of apples and Jim has 5 apples. It’s abstract. Saying “I do not have any cake” is the same as saying you have 0 cake in concept. Linguistically we use different phrasing when discussing the non quantifiable but math is a different language. Importantly- math has ways to differentiate that which is unquantifiable because it is not observable- 0 apples, I do not observe you having any apples. Non quantifiable because it is two small to express but is present or observable, non quantifiable because it is too large or it’s magnitude is not observable but is present etc.
critically thought, “0” must apply to something. It can’t exist on its own. An example is zero apples- zero applies to apples, if you had nothing you’d be naked and skinless and boneless and nonexistent-
“When you turn on a calculator it says zero- so zero is existing alone- check mate!”
Not so fast dear friend. That is zero the place holder and it never exists alone. Blank would imply nothing. A zero is there to represent that you have zero of a specific thing. In this case you have zero ones in your ones column. Place a decimal and you have 0 ones or 0 tenths and so on. We don’t always show zero and that blank doesn’t exactly represent nothing. Technically we could write “100” as “00100.0000000” or “0000000000000000000000000000000000000000000000000000000100.0000000000000000000000000” or we could put a billion or a googolplex or “infinite” zeros and never finish writing a single number.
There are exceptions to this but zero as a place holder exists as a convenience to fill relevant data fields primarily for formatting and parsing.
“Balance the equation.” This isn’t some silt rule, it’s a matter of perception and reality.
If you and I want to compare test grades, if I say I received an A, I need to know what you got to compare. If you didn’t complete the test the comparison would be an A to a did not complete. Numerically a 97 to a 0 on a points scale. This is different than if we do not know what you got- we could say 97 to X in this case or express it in writing as “97 to ?”