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Answer Posted / rahul sharma
Dijkstra explains why we should index from 0. This is a
problem on how to denote a subsequence of natural numbers,
say for example 1,2,3,...,10. We have four solutions available:
a. 0<i<11
b. 1<=i<11
c. 0<i<=10
d. 1<=i<=10
Dijkstra argues that the proper notation should be able to
denote naturally the two following cases:
1. The subsequence includes the smallest natural number, 0
2. The subsequence is empty
Requirement 1. leaves out a. and c. since they would have
the form -1<i which uses a number not lying in the natural
number set (Dijkstra says this is ugly). So we are left with
b. and d. Now requirement 2. leaves out d. since for a set
including 0 that is shrunk to the empty one, d. takes the
form 0<=i<=-1, which is a little...well, messed up!
Subtracting the ranges in b. we also get the sequence
length, which is another plus. Hence we are left with b.
which is by far the most widely used notation in programming
now.
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