what are undefined terms and also what is consistent?
 

Asked by Harshita Singh | 12th Sep, 2015, 05:56: PM

Expert Answer:

U n d e f i n e d space t e r m s colon U n d e f i n e d space t e r m s space a r e space t e r m s space w h i c h space a r e space n o t space d e f i n e d space f o r m a l l y. W e space h a v e space a c c e p t e d space t h e space t e r m s comma space P o i n t comma space L i n e space a n d space P l a n e. T h e o r e m s space a n d space P r o o f s space h a v e space b e e n space d e v e l o p e d space i n space G e o m e t r y space u sin g space t h e s e space t e r m s. R a t h e r space w e space c a n space s a y space t h a t space t h e y space a r e space b u i l d i n g space b l o c k s space o f space G e o m e t r y.  C o n s i s t e n t colon A space s y s t e m space i s space s a i d space t o space b e space c o n s i s t e n t comma space i f space h t e r e space d o space n o t space e x i s t space i n space t h e space s y s t e m space a n y space t w o space a x i o m s o r space t h e o r e m s space t h a t space c o n t r a d i c t space e a c h space o t h e r. F o r space e x a m p l e colon P a r a l l e l space l i n e s space d o space n o t space i n t e r s e c t. T h e space a b o v e space s t a t e m e n t space i s space a n space a x i o m. I n space a n y space p a r t y space o f space G e o m e t r y comma space t h e space a b o v e space a x i o m space i s space t r u e space a n d space n o space t h e o r e m space i s space t h e r e space t o c o n t r a d i c t space t h e space a b o v e space a x i o m.

Answered by Vimala Ramamurthy | 13th Sep, 2015, 08:14: AM