Zero does not exist in the same way as our concept of an "object as an entity" exists, it doesn't exist as an object. We can of course perceive zero by the absence of a particular object. For example, if I have a basket containing only 8 apples and remove 8 apples, I will have zero apples. You can't say that 1 - 1 ≠ 0.

The apples still exist.  They are just not in the basket.  This is my point. I can see people making arguments to fit what has been the convention but the conventional use of mathematics is flawed. It's limiting and unnecessary. Take away 0 and use infinity, you can then define 'pi'.

Hi sheondev,

Thanks for raising this very interesting discussion!

I have a couple of questions for you:

1. When using mathematics, we often use a particular frame of reference to apply mathematics to the real world. In the example above, I think it is generally assumed that the basket is the frame of reference, and that the number 8 is used to describe the number of apples in the basket, not all apples in existence. So, how would you describe the fact, in this system, that there are no apples in the basket?

2. How would you describe the number ten in this system?

3. How would you solve x + 5 = 8 in this system?

1.  When using the basket reference what should be done is (8+Infinity) - (8+ Infinity)= Infinity.   It is more outlandish to think (8+0) - (8+0) = 0.

Think of the colors on the electromagnetic spectrum.  What 'point' is Red, Red.  Can it really be defined so precisely?  Can it be defined to a mere 'point'? 

2.  10 is 10.  Numbers exist but there is no beginning or end.  ALL numbers are N+Infinity where N=Number.  (like, mistakenly, 1 = 1+0)

3. x + 5 = 8  ---> (x+infinity) +(5+infinity)  = (8+infinity)  just as, again, mistakenly, (x+0)+(5+0)=(8+0)

when using addition and subtract you are adding and subtracting number from infinity to infinity.  There are no negative (Imaginary) numbers. That is so ridiculous.  There is subtraction, of course, but it will never be zero, hence infinity - infinity = infinity.

Ok, I can see where you're coming from with points 1 and 3, but I don't agree with #2.

The number ten cannot be defined as 10 without relying on the concept of "zero". Place values don't really exist without the use of zero. The number ten written as "10" refers to there being one group of ten, and zero ones according to the place value. So how would you describe there being zero ones without using 0?

10 = 1010  in binary terms

10 = A    in hexidecimal terms

10 is just a point on the spectrum from   infinity ...8...9...10...11...infinity.  10 is meaningful in terms on base 10 calculations.  There is really no other significance.

I learned in 5th or 6th grade that a major role of 0 is to be a place holder. For example, 101 is different from 11. In this sense, 0 has the same purpose as 9 in 191. 9 exists and is a number, so 0 should also exist and be considered to be a number. I also learned somewhere along the line that one reason that the Roman numeral system didn't catch on is because there is no character for 0.

When I did the Cosmology and astronomy course here at Khan Academy, I learned that there is no year 0 between 1 BCE/BC and 1 CE/AD. This is an argument in favor there being no such thing as 0. But when talking about years, we need a zero, two in fact, to write out our current year, 2020 CE/AD.

Sheodev is right, there's no such thing as zero,  nor "perfect" or ultimately equal absolute numbers. Take for example this silly puzzle where 1+1 =3,

4 - 4 = 6 - 6

With equaling to zero, we have

2 × 2 - 2 × 2 = 2 × 3 - 2 × 3

2 ( 2 - 2 ) = 3 ( 2 - 2 )

take out ( 2 - 2 ) on both sides, and you have

2 = 3
or
1 + 1 = 3, which is ridiculous, just like it's ridiculous that zero exists. Always something there, there is no "nothing". Even nothing is something, therefore infinity exists. Also with the example with apples or anything, there is always something almost infinitesimally small that remains when you take away something. However, when money was invented, zero had a role for accounting etc. But again it's not "real". With the old barter system, there was always something. Zero is a ridiculous concept and invention. Some would even argue that you have no computers without zeros and ones, but zero is actually a very low voltage and one is close to 5 volts. No absolutes, ever. Except for money or other similar inventions that are "flawed" concepts as you can imagine. We may evolve into a world where zero disappears eventually, and money, injustices and other flaws may eventually go away.