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∈-induction | | ∈-induction: Encyclopedia - ∈-induction | | | In mathematics, ∈-induction is a variant of transfinite induction, which can be used in set theory to prove that all sets satisfy a given property P(x). The induction hypothesis is
for every set x, if ∀y (y∈x → P(y)), then P(x),
from which we can infer that P(x) holds for all sets x. The ...
| | | ∈-induction | | |
| | | ∈-induction: Encyclopedia - ∈-induction
∈-induction
In mathematics, ∈-induction is a variant of transfinite induction, which can be used in set theory to prove that all sets satisfy a given property P(x). The induction hypothesis is
for every set x, if ∀y (y∈x → P(y)), then P(x),
from which we can infer that P(x) holds for all sets x. The principle is equivalent to the axiom of regularity.
The name is most often pronounced "epsilon-induction", because the set membership symbol ∈ historically developed from the Greek letter ε.
 Adapted from the Wikipedia article "∈-induction", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki |
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