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Ordinal Multiplication and Exponentiation

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Please provide a detailed solution to the attached problem.

a) Suppose that alpha and Beta are non-zero ordinals such that alpha + Beta = w. What is alpha*Beta and alpha^Beta?

b) Now suppose alpha + Beta = w + 1. What are the possible values of alpha*Beta and alpha^Beta?

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Solution provided by:
Georgia Martin, PhD
Education
  • AB, Hood College
  • PhD, The Catholic University of America
  • PhD, The University of Maryland at College Park
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