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Aleph 0

One math problem a week, delivered to your inbox.

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Issues71Founded2 years agoLast Issue6 months ago
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Latest Issues

The different sizes of infinity

I will start with a somewhat provocative statement:

The set of ALL positive integers has the same size as the set of EVEN positive integers.

sounds wrong but it’s true!

At first, this sentence seems obviously wrong - I mean, one set is a...

6 months ago
66
17

What is ... a topological space?

When I was in undergrad, I was endlessly enamored with topology. I loved how it took intuitive ideas like “wiggle room” and “nearness”, and turned them into precise math.

At the heart of the subject is one notion:

the open set.

So in thi...

6 months ago
54
1

vector spaces, explained

In math, it’s very common to see two objects that look superficially different on the outside, but are actually the same on the inside.

We’ll look at two such examples in this post:

  • the 2-D plane

  • the set of real-valued continuous...

6 months ago
22
1

What is measure theory?

in search of a thesis topic …

In the early 1900s, a French graduate student named Henri Lebesgue was looking for a thesis topic.

Henri Lebesgue

He asked a very simple sounding question:

How do you measure the size of a set of points?...

7 months ago
36
5

how calculus predicts the weather

When I was in high school, my math teacher asked the class a question which I still think about quite often.

Can you show that, at any time, there are two different points on the Equator that have the same temperature?

temperature map of...

7 months ago
27
1

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