Commutative law for addition
Addition satisfies various properties that make calculations easier. The most commonly known law is the commutative law that says, for example, that
3 + 4 = 4 + 3.
It is a mistake to take commutativity for granted or think of it as a trivial observation. Note that subtraction is not commutative (3 − 4 ≠ 4 − 3). In particular, we observe a geometric difference between 3 + 4 and 4 + 3 on the following number lines even though the arithmetic outcome is the same.
3 + 4 corresponds to
4 + 3 corresponds to
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