By Julie Rowlett

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**Extra resources for Blast into Math - A Fun and Rigorous Introduction to Pure Mathematics**

**Sample text**

Blast into Math! 2. A set S is a subset of a set B if every element of S is also an element of B. ” Note that S ⊆ B is equivalent to B ⊇ S . Exercise: Practice writing S ⊆ B in different places and directions but always with the same meaning. Does this remind you of an exercise in the previous chapter? An example is: {1, 2} ⊆ {2, 1, 3, 4}, and {3, 1, 2, 4} ⊇ {2, 1}. Another example is: {1, 2} ⊆ {1, 2}. Yes, that’s right, a set is a subset of itself. So, when a set is a subset of another set, the subset is smaller but it could also be the same.

Exercise: Practice writing S ⊆ B in different places and directions but always with the same meaning. Does this remind you of an exercise in the previous chapter? An example is: {1, 2} ⊆ {2, 1, 3, 4}, and {3, 1, 2, 4} ⊇ {2, 1}. Another example is: {1, 2} ⊆ {1, 2}. Yes, that’s right, a set is a subset of itself. So, when a set is a subset of another set, the subset is smaller but it could also be the same. If we think about comparing numbers, the symbol ≤ that we use to compare numbers is similar to the symbol ⊆ that we use to compare sets.

So, if you add the smallest with the largest, 1 + 100 = 101. The next smallest player is one larger than the smallest, 1 + 1 = 2, and the next largest player is one smaller than the largest, 100 − 1 = 99. When you add them, 2 + 99 = 101. 51 Blast into Math! Sets of numbers: mathematical playground And in fact, if we keep pairing the numbers this way, each pair will always have the same sum of 101 . How many pairs are there? Since there are 100 numbers total, there are exactly 50 pairs. So, the sum of all the pairs is equal to the sum of each pair times the total number of pairs, 101 ∗ 50 = 5050.