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Functions, Part 1

• To: mathgroup at christensen.cybernetics.net
• Subject: [mg564] Functions, Part 1
• From: Jack Goldberg <Jack.Goldberg at math.lsa.umich.edu>
• Date: Fri, 17 Mar 1995 10:04:44 -0500 (EST)

Hi mathgroup:
	In trying to understand all the differences between
f[]  and  Function[]  I ran across something which puzzles me.
Consider the following:

(1)	f[x_] := x + 1

(2) 	g = Function[x,f[x]]

(3)	h = Function[x,Function[y,y+1]]

Now  g[2]  and  f[2]  output  3  as expected.  But 
h[2] (indeed, h[garbage]) outputs  Function[y,y+1].  What`s going on?
	Clearly, I do not understand exactly what happens when one 
uses the notation  Function[x,body][2]  since what I thought happens  
was this:  Every appearance of  x  in the expression "body"  is 
replaced by 2 and then body is evaluated.  In view of (3) this 
surely is not what happens.  Or am I way off base?
Jack