Expert: Paul Klarreich - 9/23/2008

Question
How do you proved that there is a one-to-one correspondence between the points of the interval [0,1]  and [-5,-3]?

Answer
Questioner:   Dwayne
Category:  Calculus
Private:  no
 
Subject:  proving one-to-one correspondence
Question:  How do you prove that there is a one-to-one correspondence between the points of the interval [0,1] and THE POINTS OF THE INTERVAL [-5,-3]?
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Hi, Dwayne,

Step 1: Use the vocabulary correctly.

Step 2: Exhibit the correspondence, as in:

Let x be a pt of [0,1].  Notice that if we double it, 2x is in [0,2], and if we shift it 5 units to the left, it is in [-5,-3].  

Then compute  2x - 5.  This is in the interval [-5,-3].  So this is your correspondence;

x in [0,1] <==>  2x - 5 in [-5,-3]

Now you just show that if two points are in [0,1], like x1 and x2, then they map to different points in [-5,-3] and vice versa.  Not difficult.