A zoomable transfinite number-line of the ordinal numbers, currently going up as far as the Bachmann–Howard ordinal φ_{εΩ+1}(0). Use the mouse to move and the left and right buttons to zoom in or out, Q or Escape quits. Note that there is currently a limit to the depth you can zoom to before the accuracy runs out.

In simple terms, for every set of transfinite numbers there is a smallest number larger than all of them, which explains why the finite numbers can be grouped together to get the first infinite ordinal ω and then this can be grouped with them to get ω+1 *and so on* (for a very long way). It is impossible to write a program to display a complete number line up to or any further than ω_{1}^{CK} (the Church–Kleene ordinal), but displays of ordinals smaller than that but larger than φ_{εΩ+1}(0) are still possible.

As well as the version below you can run previous versions up to ε_{0} (the first epsilon number) and up to Γ_{0} (the Feferman–Schütte ordinal).

Try it now! - download and run the EXE file (Windows sometimes requires you to right click, 'Properties', 'Unblock' first).

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Ordinal Number Line to φ_{εΩ+1}(0) (.7z file, 102KB; zip file, 124KB).

Use 7-Zip to open .7z files, WinZip files (less compression) provided for compatibility.

Decompress all files to a directory and run the EXE file.

Ordinal Number Line to Γ_{0} (.7z file, 72KB; zip file, 88KB).

Ordinal Number Line to ε_{0} (.7z file, 72KB; zip file, 88KB).