This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: A reminder about absolute values Math 8 2009, Chris Lyons For x R , we define the absolute value of x to be  x  = x if x  x if x < . From this definition, one can show that if C 0 then  x  C  C x C. How do you show this? Heres one direction, namely  x  C =  C x C : Assume that  x  C . There are two cases: 1. Assume x 0; then automatically we have x  C , and if we know that  x  C , then by definition (because x 0) this means x C . Thus we get both x  C and x C , meaning C x C . 2. On the other hand, if x < 0, then automatically we get x C , and from  x  C we get  x  = x C , or x  C . Thus, no matter what x is, if  x  C , then we have C x C . Ill leave it to you to show that C x C =  x  C . (Again, there are two cases to consider: (1) x 0 and (2) x < 0.) Using the previous point, if C 0 and x, y R , then we have...
View Full
Document
 Fall '08
 Vuletic,M
 Math, Calculus

Click to edit the document details