query: In the principle of Mathematical Induction, why do we take the base case as $P(1)$ only?
positive_passages.docid: 153975
positive_passages.text: Proving mathematical induction with arbitrary base using (weak) induction
negative_passages.docid: 67394
negative_passages.text: How to interpret $\mathbb{P}(B|A)$ when $\mathbb{P}(A) = 0$
negative_passages.docid: 138632
negative_passages.text: Proof that if $a > 0$, then $\frac{1}{a} > 0$ using just field and order axioms
negative_passages.docid: 4769
negative_passages.text: Any reasons why the basis case can't be at the end of a mathematical induction proof?
negative_passages.docid: 60678
negative_passages.text: Does 'A countable infinite Cartesian product of countable sets is not necessarily countable' violate induction principle?
negative_passages.docid: 133695
negative_passages.text: Induction, 0'1 and 1's sequence fun question
negative_passages.docid: 118075
negative_passages.text: What does "prove by induction" mean?
negative_passages.docid: 121544
negative_passages.text: Proof by Induction: $2(\sqrt{n+1} - \sqrt{n}) < \frac{1}{\sqrt{n}} < 2(\sqrt{n}-\sqrt{n-1})$
negative_passages.docid: 148330
negative_passages.text: Induction Proof for $F_{2n} = F^2_{n+1} - F^2_{n-1}$
negative_passages.docid: 113612
negative_passages.text: Why does $P(\theta_1\mid D, \theta_2) \propto P(D \mid \theta_1, \theta_2)P(\theta_1)$ hold?
negative_passages.docid: 68308
negative_passages.text: A (probably trivial) induction problem: $\sum_2^nk^{-2}\lt1$
negative_passages.docid: 125028
negative_passages.text: Prove the following equality using mathematical induction:
negative_passages.docid: 21035
negative_passages.text: Clarifying on how if p,q is logically equivalent to p only if q
negative_passages.docid: 70552
negative_passages.text: Prove that $\mathcal{P}(A)⊆ \mathcal{P}(B)$ if and only if $A⊆B$.
negative_passages.docid: 66971
negative_passages.text: What is the purpose of the first test in an inductive proof?
negative_passages.docid: 13012
negative_passages.text: Why can a = b imply 2 = 1?
negative_passages.docid: 87941
negative_passages.text: Prove by mathematical induction that $\forall n \in \mathbb{N} : \sum_{k=1}^{2n} \frac{(-1)^{k+1}}{k} = \sum_{k=n+1}^{2n} \frac{1}{k} $