zlacker

>>tromp+(OP)
IEEE754 64-bit representation already has infinity:

    uint64_t x = 0x7ff0000000000000ULL;
    printf("%f\n", *(double *)&x);

output:

    inf

But you could use a representation where 0 is 0, and 1 is infinity, saving 63 bits...

>>matja+5c6
Fair, but also an uninteresting answer.

>>toxik+bh6
It's about as interesting as the other answers proposed in TFA, and it gets to the meat of it: they are all just representations invented by people, and there's nothing stopping us from inventing our own representations that fit into 64 bits (or 1 bit).

>>pphysc+Zm6
No, it doesn’t. The question is “what is the largest non-trivial number you can represent with some constraint on size of its expression”. It’s a really old question, and saying “infinity” as an answer misses the point. Saying you can invent an arbitrary number system also misses the point by simply not answering. If you need to spend a bunch of bytes explaining your new system, did you really use 8 bytes?

It just feels really bad faith.

>>toxik+Zs6
What is "really bad faith" about saying "An ON bit indicates the value 'googolplex'?"

Computing is fundamentally about decoding bit strings as different arbitrary representations that are meaningful to humans.

>>pphysc+su6
Even the word "googolplex" is quite a bit longer than the lambda calculus program in question...

>>tromp+Yz6
The actual bit is just 1 though, the word "googolplex" is in the accompanying documents for interpreting the bit.

The course on reading and using lambda calculus is similarly longer than than the actual lambda calculus expression