(November 16, 2017 at 6:17 am)Kernel Sohcahtoa Wrote:

(November 16, 2017 at 4:59 am)pocaracas Wrote: So.... if we're assuming knowledge of the ^2 operator, then we should know something about it, no?
Like... it's bijective for x∈ℝ+.
1^2 = 1
2^2 = 4

So there must exist a number x ∈ ]1,2[ such that x^2 = 2.

I think I used some mean value theorem in there, but I can't remember the exact name for it.

It sounds like the intermediate value theorem: I have certainly found that theorem to be very useful when doing existence proofs, especially when trying to establish the existence of a real value for a given function on a continuous interval.  IMO, this theorem is awesome; however, it is way out of my league in the sense that I could never conceive of something like that on my own. 

In my book, the author is interested in considering the set T={t∈ℝ: t^2<2} (it is a non-empty set that is bounded above, and via the axiom of completeness, it must contain a least upper bound) and then using the definition of the least upper bound for real numbers to show that the cases x<2 and 2<x cannot happen; thus, concluding that x must equal 2.

That seems like a very far fetched way to arrive at the result... some people just like to show off, I guess!

And yep, that's the theorem I meant. It applies to continuous functions, but a bijective one gives you an extra assurance as to the uniqueness of the result.
There is an x that satisfies x^2=2 AND it is unique in ℝ+.

Yeah I'm really short too lol

Starting the fast so I can get a thingy stuck up my .............

Just picked up my car from the garage, it actually passed it's MOT test I'm so happy.

(November 16, 2017 at 5:10 am)vorlon13 Wrote: woke up sweating and figured easier to just stay up a while longer till time for another pill

really uncomfortable tonight

Having suffered such nights and taking up to 13 tablets a day (iPads are a bit difficult to swallow) with my cardiac problems. I can sympathise!

(November 16, 2017 at 9:54 am)Dave B Wrote:

(November 16, 2017 at 5:10 am)vorlon13 Wrote: woke up sweating and figured easier to just stay up a while longer till time for another pill

really uncomfortable tonight

Having suffered such nights and taking up to 13 tablets a day (iPads are a bit difficult to swallow) with my cardiac problems. I can sympathise!

Bold mine

Why would anyone want to swallow an iPad?

(November 16, 2017 at 10:02 am)Joods Wrote:

(November 16, 2017 at 9:54 am)Dave B Wrote: Having suffered such nights and taking up to 13 tablets a day (iPads are a bit difficult to swallow) with my cardiac problems. I can sympathise!

Bold mine

Why would anyone want to swallow an iPad?

You may be humor impaired. Please contact you regular physician or local comedy club.

Omg I see it now.

Sorry...I'm still out of it after hearing yesterday's news. My sense of humor is on a vacation for the time being.

(November 16, 2017 at 10:02 am)Joods Wrote:

(November 16, 2017 at 9:54 am)Dave B Wrote: Having suffered such nights and taking up to 13 tablets a day (iPads are a bit difficult to swallow) with my cardiac problems. I can sympathise!

Bold mine

Why would anyone want to swallow an iPad?

It was a joke! I like plays on words and "tablet" has basically only two meanings these days - though I suppose "tablets of stone" and Roman clay/wax tablets were forunners of iPads in a way.

(November 16, 2017 at 1:43 am)Dave B Wrote:

(November 15, 2017 at 11:17 pm)Fireball Wrote: My investment people had a client appreciation dinner last night. I came home and had such heartburn that I sat up half the night in the recliner to sleep. Too much rich food. Tired as hell, today.

Things like "client appreciation dinners" always amuse me - when they don't annoy me.

One way or the other you pay for them, either in your management fees or the profit they cream off your interest. Rather have the cash so I can have a meal with friends and not listen to propaganda!

TNSTAAFL

Oh, don't I know it! At least they're throwing a party, as opposed to just keeping that money. Hopefully it comes out of their commission   (which, of course, I paid) as opposed to the money I allegedly earned in the market. And yes, they touted "emerging markets" again this year. I haven't been real impressed with that, as it's a lot higher risk than I am prepared to invest in.