Joseph V.

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Set Theory

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Question:

How many sizes of infinity are there?

Joseph V.

Answer:

In set theory, the different sizes of infinity are called cardinals. There are infinitely many cardinals.

Discrete Math

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Question:

What is a totally ordered set?

Joseph V.

Answer:

A totally ordered set is a set where the elements of that set are ordered so that for each pair of elements x,y either x<y or x=y or x>y. For example, the real numbers form a totally ordered set.

Calculus

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Question:

Does there exist a continuous function which is not differentiable?

Joseph V.

Answer:

Yes. The absolute value function is continuous everywhere, but the absolute value function is not differentiable at (0,0) since the graph of the absolute value function has a sharp change in direction at (0,0).

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