Question

lub

Answer 1

i clearly do not understand the concept of least upper-bound

Answer 2

i think i can understand why i got the second incorrect , but i do not get the explanation for the third option

Answer 3

if a sequence(set) M is bounded \[[a,b]\]
then a,b can be treated as minimum and maximum

Answer 4

3) is incorrect because finite means it can be terminated between two values (lower and upper bound) as a subset hence the set starts smewhere and ends somewhere so it is finite

Answer 5

[0,1] means that the set is not infinite ie it is bounded between two values

Answer 6

4)\[(...-2,-1,0]\]
there is no number that is negetive after zero so it is the upper bound

Answer 7

how is the interval \([0,1]\) infinite?

Answer 8

i said not

Answer 9

i dont understand the explanation for the third option , shown in the .png

Answer 10

@Algebraic!

Answer 11

can't help sorry.. ask one of the math guys:)

Answer 12

i think i get it now.

a set is called infinite if has a an infinite number of terms in the set.

a set with a lub and a glb can still have an infinite number of terms if the set is infinitely dense ,

Answer 13

finite does not mean it can be terminated between two values ,
finite mean there are a finite number of terms

Answer 14

I think you're right on that... sounds like that describes the 3rd choice.

Answer 15

I'm less sure on "infinitely many lower bounds" (in choice # 2)

Answer 16

I suppose they're saying that if "a" is a lower bound, then any "b" less than "a" is also a lower bound. Those "b" values would not be the tightest lower bound on the set, but maybe they qualify as lower anyway?

Answer 17

a bound is simply a value that cannot be exceeded,
it is not necessary on the boundary,

Answer 18

ok, so that would make sense... if set A of reals is such that all elements of A are greater than -6, then that is one lower bound, but so are all real numbers less than -6.

Answer 19

i agree with you JakeV8

Answer 20

On that last choice, apparently the LUB of negative integers is -1, not 0... apparently the LUB can include a value that is in that set. I would have answered "0" like you did though... A least upper bound on negative integers apparently includes the greatest negative integer, -1, rather than claiming that 0 bounds the set of negative integers... it's clearly on the border, but in this case, bounding means belonging also.

I'm not sure I have a good/deep understanding of how bounds work in these cases... yet another thing to add to my list of stuff to review/remember/learn for the first time...