chose-the-right-option-1-if-x-y-Q-c-and-x-lt-y-then-a-Q-such-that-x-lt-a-lt-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-ha

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 \dots \dots .

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 \dots \dots

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 \dots \dots

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