Question

True (T) or False (F)?
Q1. Mathematical induction is used to prove statements about all real numbers. ?

Q2. Mathematical induction differs form the kind of induction used in the experimental
sciences because it is actually a form of deductive reasoning.

Q3. A proof by mathematical induction involves an inductive step, where it is
shown that a statement P(k) about a natural number k is true only if the
statement P(k+1) about its successor k+1 is true.

Q4. For a proof by mathematical induction, it is sufficient to check one base case
explicitly.

Answer 1

Mathematical induction is used to prove statements about all real numbers. ?
no it is for proving things about positive integers

Answer 2

yes that what I thought for the first one !

Answer 3

I'm not absolutely sure about Q3 - that statement must also be true for K = 1 so I think this is false.

Answer 4

- or only partly right.

Answer 5

yes I think it is false but looking at my notes and its all worded differently

Answer 6

you must prove that if the statement is true for a number kthen it is also true for k + 1

so if it is shown to be true for k = 1 then it must be tur for k = 2, 3 and so on

Answer 7

Q2 is true