mathematical induction

collocation in English

meaningsofmathematicalandinduction

These words are often used together. Click on the links below to explore the meanings. Or,see other collocations withinduction.
mathematical
adjective
uk
/ˌmæθ.əmˈæt.ɪ.kəl/us
/ˌmæθˈmæt̬.ɪ.kəl/
relating ...
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induction
noun
uk
/ɪnˈdʌk.ʃən/us
/ɪnˈdʌk.ʃən/
an occasion when someone is formally introduced into a new job or organization, especially through a ...
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(Definition ofmathematicalandinductionfrom theCambridge English Dictionary© Cambridge University Press)

Examplesofmathematical induction

These examples are from corpora and from sources on the web. Any opinions in the examples do not represent the opinion of the Cambridge Dictionary editors or of Cambridge University Press or its licensors.
The original proof was done bymathematicalinduction.
From theCambridge English Corpus
Powerful proof principles, such as equational reasoning with program terms andmathematicalinduction, are available.
From theCambridge English Corpus
He is also hailed as the first to recognize, analyze, and namemathematicalinduction.
From theCambridge English Corpus
The proof of the claim usesmathematicalinduction.
From theCambridge English Corpus
Proof bymathematicalinductionplays a crucial role in reasoning about recursively defined functions.
From theCambridge English Corpus
The prover applies a variety of symbolic manipulation techniques, including rewriting andmathematicalinduction.
From theCambridge English Corpus
We usemathematicalinductionto prove (a).
From theCambridge English Corpus
Both proofs usedmathematicalinduction.
From theCambridge English Corpus
For example, it does not prove ordinarymathematicalinductionfor all formulae, while first-order arithmetic does (it has this as an axiom schema).
From
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The non-finitistic constructions show up in the interpretation ofmathematicalinduction.
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Therefore, bymathematicalinduction, repeating this process will eventually lead to a flat folding.
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This can be easily proved withmathematicalinduction.
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For the following proof we applymathematicalinductionand only well-known rules of arithmetic.
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Continuing in this fashion, an infinite simple path can be constructed bymathematicalinduction.
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The proof is bymathematicalinductionon the exponent "n".
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Despite its name,mathematicalinductionis not a form of inductive reasoning.
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As part of this effort, he made key contributions to the modern rigorous and systematic treatment of the method ofmathematicalinduction.
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Mathematicalinduction, as formalized in the second-order axiom above, works because "k" is used to represent an "arbitrary" natural number.
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Structural recursion is a recursion method bearing the same relationship to structural induction as ordinary recursion bears to ordinarymathematicalinduction.
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For example, the second-order sentence expresses the principle ofmathematicalinduction.
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These examples are from corpora and from sources on the web. Any opinions in the examples do not represent the opinion of the Cambridge Dictionary editors or of Cambridge University Press or its licensors.
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