Question

what is the supremum of set of real nos???

Answer 1

You know what supremum means?

Answer 2

yes least uper bound

Answer 3

As a matter of fact, yes.

Can we, in fact, *bound* the set of real numbers?

Answer 4

i think no....but i have read R satisfies the property of completeness

Answer 5

and according to this property a bounded above set has a supremum

Answer 6

now what is this???

Answer 7

It means... if a set has an upper bound, then it has a least upper bound (supremum)

Answer 8

The converse is obviously true...
If a set has a least upper bound, then it has an upper bound... (proof: duh XD)

Answer 9

So... suppose the set of real numbers has an upper bound..

Answer 10

then plz tell me what is the sup of R?

Answer 11

Let's suppose there exists a real number a which is the supremum of R.

Answer 12

Then a+1 is also a real number because the set of real numbers is closed under addition.

Answer 13

a < a+1
Which already contradicts the assumption of the EXISTENCE of a supremum.

Answer 14

what is its upper bound?? infinity??? i think infinity can not be sup

Answer 15

Of course not, infinity is not a number. :D

Answer 16

then suprimum of R?

Answer 17

Does it even have one?

Answer 18

what does it mean...i could'nt understand?

Answer 19

Think of it this way... a supremum is like a maximum value...

Answer 20

So... does the set of all real numbers have a maximum?

Answer 21

yes but this is what i want to ask what is this max no??

Answer 22

Give it a good think... what is the biggest number?

Answer 23

do you know the ans???

Answer 24

As to what is the biggest number?

Answer 25

i dont know

Answer 26

can u tell??

Answer 27

can u???

Answer 28

what happens???