Unit-1 Why Learn Mathematics

This unit discusses what mathematics is, its characteristics, processes involved in developing its ideas and hierarchy of its ideas.

Prove, or disprove, the statement that every counting number is greater than or equal to the sum of its proper factors. (e.g., the proper factors of 6 are 2, 3 and 2+3 = 5.)

Answer

We can prove the given statement false with the help of a counter-example.

Consider the proper factors of 12 which are 2, 3, 4, 6.

2 + 3 + 4 + 6 = 15

15 > 12

Hence, the given statement is false.