Re: ERA question

In article <mcqdnWl5M49PAqPZnZ2dnUVZ_vOdnZ2d@xxxxxxx> on Thu, 13 Apr
2006 12:00:34 -0700, swazoo@xxxxxxx (Jeff Lichtman) wrote:

Steve wrote:
Actually, I guess I see. Basically, the limit as the denominator
approaches 0 is infinity, but at 0 it's undefined. For all intents
and purposes, you can say it's infinity, but it's technically
inaccurate. Man, five years out of high school and I forget that
already.

Generally, mathematicians avoid using the term "infinity" when they
can. The limit of X/Y as for non-zero X as Y approaches zero doesn't
exist - the limit is said to diverge.

Finite mathematics doesn't really assign a meaning to "infinity"; there
are branches of mathematics that concentrate on transfinite numbers, but
they don't get there through division by zero - and they have spotted
that aleph-null and aleph-one are different.

X/0 is said to be undefined when X doesn't equal zero. The reason is
simple: division is the inverse of multiplication, and there's
nothing that can be multiplied by 0 to give a non-zero X.

Yup.

0/0 is said to be indeterminate. Again, the reason is simple:
*anything* times zero is zero, so if you tried to assign a value to
0/0 it could be any number.

Although it is worth saying that it depends on how you get to 0/0 - 2x/x
is still 2 even if x is zero.

Having said all this, I see nothing wrong with using "infinity" as
the ERA of a pitcher with some runs allowed in zero innings. Everyone
knows what it means, and I don't know of any error in calculation or
logic that would result from its use.

Indeed, the point of avoiding the question in mathematics is that the
whole point is that we don't know what the numbers represent - or, more
accurately, that pure mathematics deals with the numbers in the abstract
without them having a meaning.

In this case, though, the ERA can be properly set to infinity, because
we aren't talking pure mathematics, but applied - and we know that this
is earned runs divided by outs (* 27). It also means that the
reciprocal comes out correctly as zero.

--
Richard Gadsden
"I disagree with what you say, but I will defend to the death
your right to say it" - Attributed to Voltaire
.

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