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Title may be hard to understand, so an example:

If a language claim to have a busy beaver function BB:unsigned int -> double, and works fine(always return Infinity when input is a bit larger and output exceed 1e+310), can we use it as one?

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  • \$\begingroup\$ When/Why would you need to use such a function? \$\endgroup\$ – user202729 Nov 20 '18 at 4:33
  • \$\begingroup\$ @user202729 Designed maybe for fun and used to generate a large number \$\endgroup\$ – l4m2 Nov 20 '18 at 7:18
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No

Languages are defined by their implementations. If the implementation doesn't work, the feature doesn't exist.

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  • \$\begingroup\$ So what's the line it differs to large memory request but without so many address wire? \$\endgroup\$ – l4m2 Nov 19 '18 at 18:05
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    \$\begingroup\$ They would work if there was more memory; lack of memory isn't the implementation's "fault". In contrast, if the program required an infinite amount of memory, it should be considered invalid. \$\endgroup\$ – Dennis Nov 19 '18 at 18:08
  • \$\begingroup\$ No they need more address \$\endgroup\$ – l4m2 Nov 19 '18 at 18:38
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    \$\begingroup\$ That's still just a hardware/OS problem. \$\endgroup\$ – Dennis Nov 19 '18 at 20:15
  • \$\begingroup\$ Consider C for example, it can only address 2^32 bytes in memory. If we move it to a 64 bit machine, it can access more than 4GB but can be considered a different implementation. \$\endgroup\$ – user202729 Nov 20 '18 at 5:16
  • \$\begingroup\$ Another problem is that Busy Beaver is calculatable with enough(but not infinite) resource \$\endgroup\$ – l4m2 Dec 2 '18 at 23:27

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