On 29 Dec 2007, at 10:14 AM, Ben Franksen wrote:
Jonathan Cast wrote:
On 28 Dec 2007, at 3:13 PM, Ben Franksen wrote:
Bulat Ziganshin wrote:
Hello Yitzchak,
Thursday, December 27, 2007, 12:10:21 PM, you wrote:
In particular,
two functions are equal only if they produce
the same value for every input, and in general it is
impossible for a computer to check that.
"for a computer" is superfluous here. people are not smarter than
computers and can't do anything that's impossible for computers
I don't think my computer can be sorry, but I know I can be.
And don't forget that there are 'undecidable' problems.
Which I have never yet seen decided by a person...
In many cases, equality of functions has been decided by humans, as
has
termination of programs. Of course this doesn't prove that humans
can, in
principle, decide equality for any pair of functions. But neither
has the
opposite been proved.
It hasn't been proved that we can't build a device that can decide
equality for arbitrary functions, either. It's simply that no one
has ever succeeded in imagining a definition of `decidable' that
includes that particular relation. I rather strongly suspect that
anything decidable by humans must be decidable in some sense...
jcc
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