I have looked at several different articles/explanations but they either have contradictory statements or they use esoteric language that I cant wrap my head around. pls help
In: Mathematics
Zero is a called an identity under addition. Under multiplication the identity is 1. Try and see the similarities and also see how it is associated with an operator: 0 with addition, 1 with multiplication.
So get any number *x*: x + 0 = x; x.1 = x. So under addition, 0 leaves your number alone; under multiplication, 1 leaves your number alone.
What’s important is to remember numbers come packaged with operators that do things to numbers. 0 has some special properties but they’re not something weird because 1 also has those properties just under a different operator. Numbers are just labels that behave a certain way with respect to operators.
That’s why you learn multiplication tables and addition tables. It’s the relationship not the labels that are important.
Now back to your question. These numbers also represent the size of a collection of things. If we have a cow, and another cow, and another one: we say there are 3 cows. What’s amazing is these labels that represent the size of collections also follow the rules of numbers. If I have 3 cows and someone gave me 2 more cows I can look at my addition tables and find 2+3 gives me 5 which amazingly is the number of cows I now have. If I gave all my cows away I now have no cows. This is 5 – 5 = 0 cows.
So 0 represents a few things. The difference between having two collections of the same number of things. The size of an empty set. The addition identity in a number system.
It wears a lot of hats – like numbers usually do. This can get it confusing if you want to go philosophical about it.
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