counting argument

how to decide what should be counted?

In combinatorics, counting argument also called double counting or counting in two ways, is a combinatorial proof technique for showing that two expressions are equal by demonstrating that they are two ways of counting the size of one set

there must be at least two left gloves or two right gloves in a group of three gloves

It is an example of a counting argument, and despite seeming intuitive it can be used to demonstrate possibly unexpected result

Taurek is trying to show that we are under no moral requirement to save five people rather than one where not all six can be saved and where there is a moral requirement to save someone. The mere fact that one group contains more people does not require us to save its members in preference to the other, smaller group. Thus the numbers don’t count, morally speaking. The apt thing to do might be to flip a coin, thus exhibiting equal concern by giving each of the six an equal chance

 abacus –, 1518&projects