[FOM] vagueness in mathematics?
Hendrik Boom
hendrik at topoi.pooq.com
Tue Mar 7 08:44:40 EST 2017
We have now seen two viewpoints on arrays and matrices.
Is this the kind of ambiguity that leads to vagueness in mathematics?
Without the discussion we just had we might never have discovered the
problem. But the discussion leads us to gain more precise concepts
than we might have had before, at least to the point of understanding
one another if not agreeing on the meanings of words.
Or is this just a termonological issue, unrelated to what we are
discussing?
I'm not sure. But it is a practical issue, arising in real life;
whereas someone thinking addition behaves differently for numbers
larger than 57 is not.
- hendrik
On Mon, Mar 06, 2017 at 11:52:40PM +0000, Annatala Wolf wrote:
> On Tue, Feb 28, 2017 at 11:55 AM Jacques Carette <carette at mcmaster.ca>
> wrote:
>
> > It is worth noting that there are similar issues elsewhere. Most
> > prominently, in computer science, most people incorrectly identify
> > arrays and matrices; but arrays are a method of memory storage, while
> > matrices are representations of (finite dimensional) linear operators
> > with respect to a given basis.
> >
...
...
>
> The short version: to a programmer, arrays are mathematical strings with a
> mathematically well-defined interface. We may also think of them as a
> method of memory storage, but this does not preclude the importance of the
> mathematical model they represent to the user. It is important to keep the
> abstract mathematical structure separate from the concrete representation,
> especially since the latter is not always certain.
> --
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