Test

[PVW]

Test

 

[Woodpecker]

 

[BobPSU92]

I plan and fail anyway.

 

[SleepyLion]

I plan and fail anyway.

And yet still exceed expectations.

 

[L.A.Lion]

 

[Nittering Nabob]

Test

Are you pregnant?

 

[LionJim]

Prove that the Least Upper Bound Property of the real number system R implies that R is complete. In other words, prove that in R every Cauchy sequence converges. (For the layman: with this result you can assume that there are no “holes” in R; the real numbers make up a solid line.)

 

[SleepyLion]

Prove that the Least Upper Bound Property of the real number system R implies that R is complete. In other words, prove that in R every Cauchy sequence converges. (For the layman: with this result you can assume that there are no “holes” in R; the real numbers make up a solid line.)

The question is, "What is something that has never been discussed in my mother's kitchen?"

... I'll take potpourri for $200, Alex.

 

[SleepyLion]

Prove that the Least Upper Bound Property of the real number system R implies that R is complete. In other words, prove that in R every Cauchy sequence converges. (For the layman: with this result you can assume that there are no “holes” in R; the real numbers make up a solid line.)

I looked up Cauchy sequences and this lead me to a way to calculate square roots. I always wondered how this was done. Thanks for that. (I'm still not in my mother's kitchen.)

 

[rudedude]

Prove that the Least Upper Bound Property of the real number system R implies that R is complete. In other words, prove that in R every Cauchy sequence converges. (For the layman: with this result you can assume that there are no “holes” in R; the real numbers make up a solid line.)

Aren’t you supposed to be drinking German beer and brandy about now?

 

[rudedude]

 

[Fac]

....icle

 

[leinbacker]

 

[LionJim]

Aren’t you supposed to be drinking German beer and brandy about now?

Had a cake and coffee break not long ago.

 

[BobPSU92]

I looked up Cauchy sequences and this lead me to a way to calculate square roots. I always wondered how this was done. Thanks for that. (I'm still not in my mother's kitchen.)

If the door to your mother’s kitchen is closed, we can assume that you are both in the kitchen and outside the kitchen.

 

[BobPSU92]

Had a cake and coffee break not long ago.

Atta boy.

 

[SleepyLion]

If the door to your mother’s kitchen is closed, we can assume that you are both in the kitchen and outside the kitchen.

There were no doors only doorways. We are both allergic to cats... not sure if we are all dead alive or both.

 

[s1uggo72]

Prove that the Least Upper Bound Property of the real number system R implies that R is complete. In other words, prove that in R every Cauchy sequence converges. (For the layman: with this result you can assume that there are no “holes” in R; the real numbers make up a solid line.)

What about the greatest lower bound?

 

[LionJim]

What about the greatest lower bound?

Easy peasy. To show that the greatest lower bound of a non-empty set A always exists, define B to be the set of all members of A times -1. (If 5 is in A, then -5 is in B. If -8 is in A, then 8 is in B.) Find the least upper bound of B, say it is x. Then -x is the greatest lower bound of the original set A.

 

[Waaaaaaaany]

Take it to the test board

 

[OhioLion]

Easy peasy. To show that the greatest lower bound of a non-empty set A always exists, define B to be the set of all members of A times -1. (If 5 is in A, then -5 is in B. If -8 is in A, then 8 is in B.) Find the least upper bound of B, say it is x. Then -x is the greatest lower bound of the original set A.

Both your posts in this thread gave me a headache, and reminded me of why the highest level of math I taught was 6th grade.