Mathematical Concepts Flashcard

Front

Statement of the Continuum Hypothesis (CH)?

Back

There is no set whose cardinality is strictly between that of the integers and the real numbers.

Front

The real numbers are constructed through which of the following methods?

Back

Dedekind cuts or Cauchy sequences.

Front

What is the cardinality of the continuum?

Back

Uncountably infinite.

Front

The integers are constructed from which of the following sets? The set of natural numbers., The set of real numbers., The set of rational numbers., The set of complex numbers.

Back

The set of natural numbers.

Front

How are rational numbers constructed from the integers?

Back

As pairs of integers, with the second element non-zero.

Front

Which operation is used to construct real numbers from rational numbers?

Back

Dedekind cuts or Cauchy sequences.

Front

What is an ordinal number?

Back

A number used to indicate the position of an element in a well-ordered set.

Front

Example of an ordinal number: 1, 2, ω (omega), √2

Back

ω (omega)

Front

What is true about the ordinal number ω?

Back

It represents the first infinite cardinal number.

Front

Key feature of transfinite induction?

Back

It is a method of proof for inductive statements over well-ordered sets.