Question
Thu April 09, 2015 By: Mehr Arora

what is an interval notation?
 
why can't an element of a set be a subset of itself?

Expert Reply
Vimala Ramamurthy
Fri April 10, 2015
C o n s i d e r space t h e space f o l l o w i n g space i n e q u a l i t i e s colon  0 less or equal than x less than 10 comma space x element of R H e r e comma space x space c a n space t a k e space v a l u e s space f r o m space 0 space t o space 9.999999.... space a n d space x equals 10 space i s space n o t space a n space e l e m e n t space o f space t h e space s e t T h i s space i s space a l s o space r e p r e s e n t e d space a s space left square bracket 0 comma 10 right parenthesis I n space t h e space n u m b e r space l i n e comma space 0 space i s space m a r k e d space w i t h space s o l i d space d o t space a n d space 10 space i s space m a r k e d space w i t h space t r a n s p a r e n t space d o t.  minus 1 less than x less or equal than 5 comma space x element of I H e r e comma space x space c a n space t a k e space v a l u e s space f r o m space 0 space t o space 5 space a n d space x equals negative 1 space i s space n o t space a n space e l e m e n t space o f space t h e space s e t T h i s space i s space a l s o space r e p r e s e n t e d space a s space left parenthesis negative 1 comma 5 right square bracket I n space t h e space n u m b e r space l i n e comma space minus 1 space i s space m a r k e d space w i t h space t r a n s p a r e n t space d o t space a n d space 5 space i s space m a r k e d space w i t h space s o l i d space d o t.  15 less than x less than 16 comma space x element of R H e r e comma space x space c a n space t a k e space v a l u e s space f r o m space 15.000001... space t o space 15.99999999 space a n d space x equals 15 space a n d space x equals 16 space a r e space n o t space t h e space e l e m e n t s space o f space t h e space s e t T h i s space i s space a l s o space r e p r e s e n t e d space a s space left parenthesis 15 comma 16 right parenthesis I n space t h e space n u m b e r space l i n e comma space b o t h space 15 space a n d space 16 space a r e space m a r k e d space w i t h space t r a n s p a r e n t space d o t s.  1 less or equal than x less or equal than 25 comma space x element of N H e r e comma space x space c a n space t a k e space v a l u e s space f r o m space 1 space t o space 25. T h i s space i s space a l s o space r e p r e s e n t e d space a s space left square bracket 1 comma 25 right square bracket I n space t h e space n u m b e r space l i n e comma space b o t h space 1 space a n d space 25 space a r e space m a r k e d space w i t h space s o l i d space d o t s.  C o n s i d e r space t h e space s e t space A equals open curly brackets 1 comma 2 comma 3 comma 4 comma 5 close curly brackets H e r e comma space 1 comma 2 comma 3 comma 4 space a n d space 5 space a r e space t h e space e l e m e n t s space o f space t h e space s e t. B u t space 1 comma space 2 comma space 3 comma 4 space a n d space 5 space a r e space n o t space t h e space s u b s e t s space o f space A S u b s e t s space o f space A space c a n space h a v e comma space open curly brackets 1 close curly brackets comma space open curly brackets 2 close curly brackets comma space open curly brackets 3 close curly brackets comma space open curly brackets 4 close curly brackets comma.... open curly brackets 1 comma 2 comma 3 close curly brackets comma space open curly brackets 1 comma 4 comma 5 close curly brackets T h u s comma space a n space e l e m e n t space o f space a space s e t space n e e d space n o t space b e space a space s u b s e t space o f space i s e l f.
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