Paxtonvic’s Blog

Just another weblog

Just slept through….

A whole programme on BBC 2 about infinity………I’m sure that it proved the existence of God though without explicitly trying to do so. How about the idea that versions of us co-exist somewhere out in space????

The Lemniscate, ∞, in several typefaces.

The precise origin of the infinity symbol, \infty, is unclear. One possibility is suggested by the name it is sometimes called—the lemniscate, from the Latin lemniscus, meaning “ribbon”

Actually, the whole theory about infinity is very simple… it goes like this:

In real analysis, the symbol \infty, called “infinity”, denotes an unbounded limit. x \rightarrow \infty means that x grows without bound, and x \rightarrow -\infty means the value of x is decreasing without bound. If f(t) ≥ 0 for every t, then

  • \int_{a}^{b} \, f(t)\ dt \  = \infty means that f(t) does not bound a finite area from a to b
  • \int_{-\infty}^{\infty} \, f(t)\ dt \  = \infty means that the area under f(t) is infinite.
  • \int_{-\infty}^{\infty} \, f(t)\ dt \  = n means that the total area under f(t) is finite, and equals n

Get it?

I remember asking a teacher once what infinity was… and she just went on and on and on…

February 10, 2010 - Posted by | Uncategorized

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