Archive
16th of September 2015
Mathematics
Q:

can u explain me all the properties of integers like

(closer pro.1)

Aditya Saxena - CBSE - Class VII

Tuesday, September 15, 2015 at 20:43:PM

A:

C l o s u r e space p r o p e r t y colon L e t space a comma b element of Z comma space T h e n space a plus b element of Z space a n d space a cross times b element of Z E x a m p l e colon space 3 comma negative 1 element of Z comma space t h e n space 3 plus open parentheses negative 1 close parentheses equals 2 element of Z space a n d space 3 cross times open parentheses negative 1 close parentheses equals negative 3 element of Z H e n c e space t h e space s e t space o f space I n t e g e r s space i s space c l o s e d space u n d e r space a d d i t i o n space a n d space m u l t i p l i c a t i o n.  C o m m u t a t i v e space p r o p e r t y colon L e t space a comma b element of Z. I f space a plus b equals b plus a comma space a cross times b equals b cross times a comma space t h e n space a comma b space a r e space c o m m u t a t i v e space u n d e r space a d d i t i o n space a n d space m u l t i p l i c a t i o n. E x a m p l e colon space 4 comma negative 2 element of Z comma space t h e n space 4 plus open parentheses negative 2 close parentheses equals open parentheses negative 2 close parentheses plus 4 equals 2 space a n d space 4 cross times open parentheses negative 2 close parentheses equals open parentheses negative 2 close parentheses cross times 4 equals negative 8  A s s o c i a t i v e space p r o p e r t y colon L e t space a comma b comma c element of Z. space a plus open parentheses b plus c close parentheses equals open parentheses a plus b close parentheses plus c space a n d space a cross times open parentheses b cross times c close parentheses equals open parentheses a cross times b close parentheses cross times c  I d e n t i t y space p r o p e r t y colon L e t space a comma space e element of Z I f space a plus e subscript 1 equals e subscript 1 plus a equals a space a n d space a cross times e subscript 2 equals e subscript 2 cross times a equals a H e r e space 0 space i s space t h e space a d d i t i v e space i d e n t i t y space a n d space 1 space i s space t h e space m u l i p l i c a t i v e space i d e n t i t y space o f space t h e space s e t space o f space i n t e g e r s.  I n v e r s e space p r o p e r t y L e t space a element of Z T h e n space a d d i t i v e space i n v e r s e space o f space a space i s space minus a

Wednesday, September 16, 2015 at 18:13:PM