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The surreal numbers
The big bang of numbers
On the big bang of numbers, the surreal genesis—an excerpt from my podcast with Lex Fridman, a sweeping conversation on infinity, philosophy, and…
Apr 23
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Joel David Hamkins
8
1
The surreal line is topologically compact—or is it?
Shocking instances of compactness in the surreal line
Nov 28, 2025
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Joel David Hamkins
12
2
5
The surreal line is topologically disconnected—or is it?
The surreal line is topologically disconnected according to a natural conception of connectedness. Nevertheless, on another conception—attending to…
Nov 15, 2025
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Joel David Hamkins
12
8
4
The omnific integers are strange
We shall explore several surprising failures of the analogy between the omnific integers and the integers. It turns out that Oz is not so very like ℤ…
Nov 4, 2025
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Joel David Hamkins
11
7
4
The omnific integers are an integer part of the surreal numbers
Can we find a surreal-numbers analogue of the integers? An integer part of the surreal numbers, a discretely ordered subring, for which every surreal…
Oct 23, 2025
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Joel David Hamkins
13
4
6
The surreal ω × ω chessboard is bigger than you think
What is the nature of the surreal ω × ω chessboard? How many squares are there? How many chess pieces shall we require to set up the board?
Oct 13, 2025
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Joel David Hamkins
10
13
6
The surreal numbers
All the numbers great and small. The surreal numbers, generated in a recursive process of completion, unify the real numbers, the ordinals, and the…
Jan 6, 2024
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Joel David Hamkins
39
6
5
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