Induction Definition/Meaning:

A process for proving mathematical statements involving members of an ordered set (possibly infinite). There are various formulations of the principle of induction. For example, by the principle of finite induction, to prove a statement p(i) is true for all integers i ≥ i₀ , it suffices to prove that

(a) P(i₀) is true;

(b) for all k ≥ i₀ , the assumption that P(k) is true (the induction hypothesis) implies the truth of P(k+1).

(a) is called the basis of the proof, (b) is the induction step.

Generalizations are possible. Other forms of induction permit the induction step to assume the truth of P(k) and also that of

P(k-1), P(k-2), ...., P(k-i)

for suitable i. Statements of several variables can also be considered.

Near by Terms: Inactive Incidence Matrix Incompleteness Theorems Incremental Compiler Incremental Plotter Indeterminate System Index Indexed Addressing (indexing) Indexed File Index Register Indicator Indirect Addressing Induction Inequality Inference Infix Notation Information Information Hiding Information Management System Information Processing Information Storage and Retrieval Information Structure Information System Information Technology (IT) Information Theory INGRES Trademark Inherent Addressing Inherently Ambiguous Language Inhibit Initial Algebra Initialization Injection (one-to-one function) Ink Jet Printer In-Line Program Inner Code Inorder Traversal Input Input Area Input Device Input-Limited Process Input/Output (I/O) Inquiry Station Inscribe Insert Instantiation Instruction (instruction word) Instruction Counter (current address register; program counter) Instruction Cycle Instruction Format  Instruction Register Instruction Repertoire Instruction Sequencing Instruction Set Instruction Stream Integer Multiplication and Division Integrated Circuit (IC) Integrated Injection Logic Integrity Intel Intelligent Copier Intelligent Terminal Interactive Interactive Graphics Interblock Gap (IBG) Interface Interior Path Length of a Tree Interleaving Interlock Intermediate Storage Internal Fragmentation Internet Protocol (IP) Internetworking   Interpolation Interpreter Interpretive Language Interrogation     Interrupt Interrupt Handler (IH) Interrupt I/O Interrupt Mask Interrupt Priority Intersegment Linking Interval Tuner Intrinsic Semiconductor (i-type semiconductor) Invariant Inverse Matrix Inverted File Inverter (negator) Involution Operation