Question

1. How do you construct an inductive proof?
2. What does it mean for a set to be closed under an operation?
3. What is set union?
4. What is set intersection?
5. What is another name for the intersection of all inductive sets?
6. What is formalism?

Answer 1

1. It is basically just as every other proof where each step is justified , In proof by induction we take a number n try to prove it for n=1 and then w eassume it to be true for n = k and then we show it is true for n = k+1.

2. A set is closed under operations means if any operation done on the two elements in the set produces another element which belongs to the same set then it is closed under operation.

3. The union of two sets is the set containing all elements of both the sets.

4. For two sets , intersection of sets takes only the elements that are in both the sets.

5. The intersection of all inductive sets is the set of natural numbers.

6. Formalism means mathematics can be reduced to rules in order to manipulate formulas without providing any reference to the meanings of the formulas.