Regular Expression for numerical constant

Question

In Sipser's book of Theory of computation, following is given :

a numerical constant that may include a fractional part and/or a sign may be described as a member of the language

( + U - U e) (D+ U D+ . D* U D* . D+)

where D = {0,1,2,3,4,5,6,7,8, 9} is the alphabet of decimal digits. Examples of generated strings are: 72, 3.14159, +7 ., and -.01 .

Here I can't understand what is the purpose of taking union of D+ or D* ? Moreover why 3rd dot is added?

Please someone clear my doubt.

Answer 1

It's trying to cover the following cases:

5    #matched by D+
.5   #matched by D*.D+
5.   #matched by D+.D*
5.5  #matched by both D*.D+ and D+.D*
.    #not matched

The . character in the expressions is the decimal separator. You can read the expression this way:

( + U - U e) ( (D+) U (D+ . D*) U (D* . D+) )