alt Hacker NewsIs it though? All languages have the word 'nothing'.
Better candidates: a) place-value numbering aka the positional numeral system, b) the Cartesian coordinate system. Forced to choose, I would pick (b).
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Asraelite • today at 12:23 PM
"nothing" is not the same the same as "zero". "zero apples" means something different to "nothing", but that difference is subtle and difficult to explain, which is what makes the invention of zero such an achievement.
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throw0101a • today at 2:38 PM
> Is it though? All languages have the word 'nothing'.
The interpretation of the concept that been different over time. See perhaps The Nothing That Is: A Natural History of Zero by Kaplan:
The difference is that zero is explicitly a number, rather than a concept.
Making it a number allows it interact with the rest of mathematics in a consistent way, which I'd argue you can't do with "nothing".
To use your later example of "no apples":
Is no apples the same thing as no bananas? What about no meters? I honestly don't know, the question is a bad one. My gut says yes, nothing in each case is just nothing.
Is zero apples the same thing as zero bananas or zero meters? No, they're different because the unit "apple" is orthogonal to the unit "meter".
The precision of zero is what's so special about it.