A zoomable transfinite number-line of the ordinal numbers, currently going up as far as the extended Buchholz ordinal ψ0(ΩΩΩ...). 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 ω1CK (the Church–Kleene ordinal), but displays of ordinals smaller than that but larger than ψ0(ΩΩΩ...) are still possible.
As well as the version below you can run previous versions up to ε0 (the first epsilon number), up to Γ0 (the Feferman–Schütte ordinal) and up to φεΩ+1(0) (the Bachmann‐Howard ordinal).
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Windows Ordinal Number Line to ψ0(ΩΩΩ...) (.7z file, 229KB; zip file, 298KB).
Linux Ordinal Number Line to ψ0(ΩΩΩ...) (.7z file, 222KB; tar.gz file, 281KB).
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 φεΩ+1(0) (.7z file, 102KB; zip file, 124KB).
Ordinal Number Line to Γ0 (.7z file, 72KB; zip file, 88KB).
Ordinal Number Line to ε0 (.7z file, 72KB; zip file, 88KB).
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