http://friam.383.s1.nabble.com/Tweet-from-MathType-MathType-tp7596925p7596944.html
Tom,
Reflecting a bit more, there are other places in
mathematics where similar ideas arise. Consider
a series like:
1 + 1/2 + 1/4 + 1/8 + ...
mathematicians will often wish to treat these infinite sums
as if they were lists. One thing to do with a list is to pop
the head from the list and return just the tail. Multiplying the
list by 1/2 does exactly this:
1/2 (1 + 1/2 + 1/4 + 1/8 + ...)
Now I have just the same list but without the head.
Manipulations like this one are more-or-less part of the
machinery for working with a series. Another classic
example are the pair of functions div and mod. The first
of these acts like division but only gives back the integer
part (quotient), thus div 4 25 is 6. mod on the other
hand is a function which returns the remainder, 1 here.
Now given a number like 273427893045 in base 10,
we can use mod 10 to pop the 5 off the end of the
number as-if-it-were a list and div 10 to return the
rest of the number as-if-it-were a list. Examples like
these are ubiquitous in mathematics and are in part
what makes the whole project seem like black magic
or index twiddling. Really, they are perhaps just conveniences
that arise via analogies between one domain of mathematics
and another. The Iverson bracket is similarly one such device,
connecting logic (Bool) to number (Int).
Jon
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