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CBSE Class 12-science Answered

If possible define a bijective mapping from straight natural numbers to straight integer numbers
Asked by yugibo | 13 Apr, 2016, 10:21: PM
answered-by-expert Expert Answer
f left parenthesis x right parenthesis equals open curly brackets table attributes columnalign left end attributes row cell x over 2 comma space x space i s space e v e n space n a t u r a l space n u m b e r end cell row cell fraction numerator 1 minus x over denominator 2 end fraction comma space x space i s space o d d space n a t u r a l space n u m b e r end cell end table close
H e r e space e v e n space n a t u r a l space n u m b e r s space g i v e space p o s i t i v e space i n t e g r a l space v a l u e s space o f space f left parenthesis x right parenthesis.
O d d space n a t u r a l space n u m b e r s space g i v e space n e g a t i v e space i n t e g r a l space v a l u e s space a n d space apostrophe 0 apostrophe space a s space v a l u e space f o r space f left parenthesis x right parenthesis.
T h e space f u n c t i o n space i s space o n e minus o n e space a n d space o n t o. space H e n c e comma space b i j e c t i v e.
Answered by satyajit samal | 15 Apr, 2016, 12:18: PM
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