Which was a revolution. From Megan Gannon at LiveScience:

The concept of zero as a number was revolutionary in mathematics. Historians have long known the idea came from India, but its exact origins remain murky.

Now, the oldest Indian reference to the digit zero has been identified, in a manuscript dating back to the third or fourth century, scientists at the University of Oxford in England announced.

…

The concept of zero as the number representing absolute nothingness paved the way for algebra, calculus and computer science. The first text to discuss zero in the numerical sense is the Indian astronomer Brahmagupta’s work “Brahmasphutasiddhanta,” which was written in A.D. 628.More.

Zero is an abstraction, not a number (it corresponds to nothing), which makes its role all the more interesting…

*See also:* Is zero even?

Zero is an abstraction, not a number (it corresponds to nothing), which makes its role all the more interesting…False. All numbers, including members of the sets natural, real, imaginary, and complex, are part of a associated ordered field. Each number is considered a position (or point) in its field. By definition, zero, being a position (or point), is a number. It’s not arguable in the slightest.

Lets do a thought experiment. I give you an old lead acid battery say 20 years old. You could assume a measurement at the terminals would be zero volts. Whether the terminals exhibit zero volts has nothing to do with the “nothing” as ballyhoo’d in the article. The voltage measure might not even be zero. even if extremely close to zero. You would have no real way to distiguish between battery internal voltage and thermocouple effects in the measuring circuit among the metals of the conductors in the circuit. Thus zero is just one of the points along the real number line representing the voltage measured. Your instrument might actually register zero while being in error by some amount even if a few picovolts.

As an abstraction though zero does have a special place, say in the complex plane, where zero is the point referred to as the origin, where it demarcates positive values from negative in each dimension.

But to keep things as simple as possible if you are interested, read the wikipedia article on real numbers to understand the concept of ordered field:

https://en.wikipedia.org/wiki/Real_number

Zero is indeed a number as its role in the von Neumann construction of the naturals shows:

{} –> 0

{0} –> 1

{0,1} –> 2

{0,1, 2} –> 3

etc

groovamos & kf – I guess one could conclude that all numbers are abstractions.

Agree with Groovamos. Zero as a number is NOT the same thing as a place-holder meaning nothing.

The place-holder mark still exists and still serves its original purpose. When you fill out a detailed form and put — in the blanks that aren’t relevant, you’re using the place-holder mark. A mark that means “I don’t have any children” is not the same as “0 children”, because 0 is just the midpoint of a two-way continuum. If you put 0 in the blank, you would be indicating that your present child-count happens to be in the middle of the continuum, but you could have +2 kids or -3 kids at some time in the future. Negative kids are certainly common, but -kids are not physically or logically possible.

In computerish terms, the place-holder mark — is more like a NULL variable, not a variable set equal to zero.

BO’H: in the sense of not concrete material entities, yes. But such are very real and constrain possibilities of being and non-being. KF

Dean:

But neither zero nor the negative numbers correspond to reality the way in the same way the positive integers do.This too is false, simply based in measurement theory. Simple example: Even a cheap voltmeter will distinguish negative from positive. My thought experiment above did not specify which polarity to hook up the test leads because it does not matter, the measurement accounts for both polarity of reals. This is true for all types of measurement and instruments for such. This is reality. Once you designate the polarity of something, its negative exists. You designate the angular velocity polarity of a driveshaft for example, there is a positive velocity demarcated from the reverse direction which is negative. Just because the ancients didn’t see this does not mean it is not reality.

Groov, vectors, where of course complex numbers are vectors and we then go to rotating vectors. KF

Dean @6

I love your thought “I borrow zero,negative numbers, and infinity from God”. I very much think along the same lines about zero and infinity. But would like to get your thought on negative numbers. When I see a number describing reality in a point in time, then I agree, no negatives. But when I describe the change between two realities– I have 10 apples yesterday, I gave 2 away, and I have 8 apples now — then the negative is a very real description of reality. Doesn’t seem like I’m borrowing just a “thought experiment” like zero and infinity. See what I’m saying? Would like your thoughts on negative numbers when we apply them to change of states.

Juwilker

Dean,

Thanks for that explanation. I see what you are saying. There are two kinds of realities that we can describe. Static and movement. Negatives will only come with the movement reality. My background is in finance. So I can relate the “static” reality like an entity’s balance sheet: a list of their assets and liabilities at a point in time. Any negative numbers on the balance sheet are simply a demarcation issue, but do not describe reality. Anyone retorting “but what about negative equity?” should understand there is no such thing. Negative equity is akin to a man holding 10 applies telling the man next to him that if he could only get 5 more apples he would have 15.

The “movement” reality is likened to an entity’s income statement: a flow of dollars over a period of time. Negative numbers on the income statement are “real” for purposes of the income statement; but as you say, they only describe the change in dollars/assets/liabilities, but not the dollars/assets/liabilities themselves.

Enjoyed your thoughts about zero, infinity, and negatives. These numbers should make us pause and humbly thank our Lord for allowing us to think his thoughts after him.

Juwilker