Category:Principle of Finite Induction
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This category contains pages concerning Principle of Finite Induction:
Let $n_0 \in \Z$ be given.
Let $\Z_{\ge n_0}$ denote the set:
- $\Z_{\ge n_0} = \set {n \in \Z: n \ge n_0}$
Let $S \subseteq \Z_{\ge n_0}$ be a subset of $\Z_{\ge n_0}$.
Suppose that:
- $(1): \quad n_0 \in S$
- $(2): \quad \forall n \ge n_0: n \in S \implies n + 1 \in S$
Then:
- $\forall n \ge n_0: n \in S$
That is:
- $S = \Z_{\ge n_0}$
Subcategories
This category has only the following subcategory.
S
Pages in category "Principle of Finite Induction"
The following 13 pages are in this category, out of 13 total.
P
- Principle of Finite Induction
- Principle of Finite Induction for Peano Structure
- Principle of Finite Induction/One-Based
- Principle of Finite Induction/One-Based/Proof 1
- Principle of Finite Induction/One-Based/Proof 2
- Principle of Finite Induction/Peano Structure
- Principle of Finite Induction/Proof 1
- Principle of Finite Induction/Proof 2
- Principle of Finite Induction/Zero-Based
- Principle of Weak Finite Induction
- Proof by Finite Induction