Timeline for Comparing really big numbers
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 15, 2015 at 22:27 | comment | added | Gerry Myerson | There are some small numbers for which it is very difficult to decide which one is bigger, e.g., one-half, and the number of zeros of the zeta function in the critical strip but off the critical line. | |
| Nov 15, 2015 at 15:36 | answer | added | Jacques Carette | timeline score: 3 | |
| Nov 15, 2015 at 3:38 | comment | added | ARi | If there is such a function it can not be 'total'. Producing a result on every input pair would effectively enable one to decide if an arbitrary mu recursive function terminates. | |
| Nov 14, 2015 at 21:10 | comment | added | Garabed Gulbenkian | I can imagine the existence of a theory T which is an extension of Peano's Arithmetic (PA). Further T could be consistent if PA is. In T the relation "bigger than " could then be defined. There might be two numbers "a" and "b" which are both definable in T, whose definitions are such that each of the statements "a is bigger than b" and "b is bigger than a" are unprovable in T but are consistent with T when added as axioms to T. | |
| Nov 14, 2015 at 20:26 | comment | added | James Propp | I agree, but how does this relate to the question? I was asking about a routine that accepts as input a pair of definitions of natural numbers (like a googolplex and Graham's number) and outputs a single bit that says which one is bigger. So the notion of a "bigger output" does not immediately apply. | |
| Nov 14, 2015 at 18:42 | comment | added | ARi | Given any such system there is always another which will produce a bigger output when given the same input. One way it can be seen is through a diagonal argument. | |
| Nov 14, 2015 at 16:59 | answer | added | Stella Biderman | timeline score: 0 | |
| Nov 14, 2015 at 14:38 | history | asked | James Propp | CC BY-SA 3.0 |