Saturday, January 05, 2008

Still under the weather

Today I feel infinitely worse than yesterday. Anyone have any tricks up their sleeves to get this bean back up an running? I have had some Beechams, but they don't seem to have had any effect. Unfortunately I can become one of the biggest babies alive on this planet at times, and now is one of them times! Alas my neck is stiff and my head is throbbing. Worry not though, I am now going to rest my eyes repeating the following definition:

Definition
Let f: A \to \mathbb{R} be a function whose domain A contains a deleted neighbourhood of a \in \mathbb{R}.

The limit of f at a \in \mathbb{R} is L if, and only if for all \varepsilon \text{\textgreater  } 0, there exists a \delta \, \text{\textgreater  }\, 0 such that if, 0 \, \text{\textless  }\, |x-a| \, \text{\textless  }\, \delta then  |f(x)-L| \, \text{\textless  }\, \varepsilon.

That is: \forall \varepsilon \, \text{\textgreater  }\, 0, \exists \,\delta \, \text{\textgreater }\, 0: 0 \, \text{\textless  }\, |x-a| \, \text{\textless  }\, \delta \Rightarrow   |f(x)-L| \, \text{\textless  }\, \varepsilon. (Which is sometimes written as f(x) -> L as x-> a.)

It is my hope that when my eyes open, I will be miraculously better and then attack real analysis with some energy. I wouldn't mind a dash of adrenaline though. Did I mention that I hate coughing? Sneezing is much more... elegant shall we say! (Well it doesn't sound as harsh as coughing does it?) Oh and for the record, one can become sick of Weetabix.

Anyway, let us hope that I feel better soon so that today goes to waste as well. (As did yesterday). Do you think sitting in one place, wrapped up in a blanket, makes it worse? I mean delay recovery. It feels so much better though, than running around like a lunatic (as per usual). Yes, I will shut up now. I have something remarkable which I would like to post, but my battery is not going to last long enough for me to do so! (OK, that was my lame attempt at using Fermat's cheeky comment in the margin). Truth be told it isn't that remarkable a thing, but it made my mum wonder "what are we going to do with you beans"!

Good night...

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