

Recipricol of infinity
Name: vernon k gambleton
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Question:
Isn't the reciprocal of infinity equal to zero?
....1/(1/2)=2,1/((1/8)=8, so as the denominator gets close to
zero the number gets bigger.
Replies:
Yes, but mathemeticians like to confuse people, so they pretend that
they don't know what you mean by "infinity". Most physicists will agree
with me.
jlu
I guess that puts me in a quandary since I majored in Mathematical Physics!
Just one more thought that I hope won't further obfuscate this issue:
infinity as a number is not a member of the set of integers, rationals,
or Reals. If you want to get further into this, look up "cardinality"
and "denumerable" and "nondenumerable" sets.
Have fun! ;)
hawley
The important thing is not to let the language obscure the concept.
The question actually is:
What is the limit of 1/x as x grows monotonically without bound?
and it is probably asked by someone who is just beginning to learn
algebra. We can reformulate the question and answer in the language
of set theory and mappings, I suppose, but who is helped by that? The
simple answer, "zero", would seem to suffice.
I quote Steve Weinberg, "Gravitation and Comology", p. 114:
"...mathematicians have developed a general formalism, known as the
. Unfortunately, the rather abstract and
compact notation associated with this formalism has in recent years
seriously impeded communication between mathematicians and physicists."
The essence of physics has always been communication, rather than
mathematical rigour. The test I use for myself is that if I can't
explain a concept in language that a 4th grader can understand, then
I probably don't understand the concept very well myself.
Oh, yes, I have been publishing papers in mathematical physics for
almost 40 years.
jlu
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Update: June 2012

