chose the right option 1) if x,y ∈Q^c and x<y then ∃a∈Q such that x<a<y in case we say that a)Q^c is an ordered field b)Q dense inQ^c c)not ordered field 2)let Q≠A ∈ Q,A not necessary has least upper bound and greatest lower bound that mean (Q,+,.,≤)is....... a)not complete b)complete c)dense in R 3)the sequence a_n =(n/(n+1)) is convergent to...... a)0 b)1 3)∞ 4) let f:A→B be a real valued function and Q≠S⊆A such that f is not continuous on S then f is a)contiuous on A b) continuous at any points x_0 in A c) continuous on A/S 4)every set of natural numbers has a least element so the order set of natural number is...... a)bounded from above b)bounded from below c)well ordered


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Question Number 88607 by M±th+et£s last updated on 11/Apr/20

$c h o s e t h e r i g h t o p t i o n$ $1) i f x, y \in Q^{c} a n d x < y t h e n \exists a \in Q$ $s u c h t h a t x < a < y i n c a s e w e s a y t h a t$ $a) Q^{c} i s a n o r d e r e d f i e l d$ $b) Q d e n s e {i n Q}^{c}$ $c) n o t o r d e r e d f i e l d$ $2) l e t Q \neq A \in Q, A n o t n e c e s s a r y h a s$ $l e a s t u p p e r b o u n d a n d g r e a t e s t l o w e r$ $b o u n d t h a t m e a n (Q, +, ., ⩽) i s . . . . . . .$ $a) n o t c o m p l e t e$ $b) c o m p l e t e$ $c) d e n s e i n R$ $3) t h e s e q u e n c e a_{n} = \frac{n}{n + 1} i s c o n v e r g e n t$ $t o . . . . . .$ $a) 0$ $b) 1$ $3) \infty$ $4) l e t f : A \to B b e a r e a l v a l u e d f u n c t i o n$ $a n d Q \neq S \subseteq A s u c h t h a t f i s n o t c o n t i n u o u s$ $o n S$ $t h e n f i s$ $a) c o n t i u o u s o n A$ $b) c o n t i n u o u s a t a n y p o i n t s x_{0} i n A$ $c) c o n t i n u o u s o n A / S$ $4) e v e r y s e t o f n a t u r a l n u m b e r s h a s$ $a l e a s t e l e m e n t s o t h e o r d e r s e t o f$ $n a t u r a l n u m b e r i s . . . . . .$ $a) b o u n d e d f r o m a b o v e$ $b) b o u n d e d f r o m b e l o w$ $c) w e l l o r d e r e d$
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