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Skill 2 of 14
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# Subtraction

The bagel store is 5 kilometres from home. School is 3 km from home. Drive on your bike from school to the bagel store, and you are moving 2 kilometres further away from home:

$$s_\text{end}- s_\text{start}=5\,\mathrm{km}-3 \,\mathrm{km} =2 \,\mathrm{km}$$

We have here reused the dash ($\,-\,$) from the negative sign as a minus symbol to be able to subtract two numbers from each other.1 We can call this operation subtraction.

These 2 kilometres are the difference between where we started and where we will end. Let’s invent a symbol to mean ‘difference’ to be able to write it shorter; why not the Greek letter Delta $\Delta$.2 Then, writing $\Delta s$ means: ‘the difference from what $s$ was to what it is now’, in short: ‘the difference in $s$’:

$$\Delta s=\underbrace{5\,\mathrm{km}}_{s_\text{end}}- \underbrace{3\,\mathrm{km}}_{s_\text{start}} =2\,\mathrm{km}$$

Note that a ‘difference’ is ‘end-distance minus start-distance’:

• We look at where we end ($s_\text{end}$),
• and subtract everything up until where we started ($s_\text{start}$).
• Then we only have that left, which is in between start and end.

The difference-symbol $\Delta$ can of course also be used for other properties, for example time $\Delta t$ (that is, the difference between start- and end-moments, meaning how much time that passed).

References:

1. διαφορά’ (encyclopedia), Wiktionary, 2017, www.wiktionary.org/wiki/διαφορά (accessed Aug. 5th, 2019)