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My Key Properties of Addition
Here are what I think of as some of the key properties of addition:
- addition is associative: (2+3)+4=2+(3+4)
- addition is commutative: 2+3=3+2
To say more, we need to think about what kinds of things we are adding.
If we are allowed to use all the integers, addition has the following important properties:
- there is an integer, 0, which acts as an identity element.
This means that adding 0 to a number does nothing: 2+0=2.
- for every integer there exists an integer so that there sum is zero.
That is to say, every integer has an inverse. For example,
2+(-2)=0.
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