Infinity

It's natural for us to see things from a start to and end. The concept of eternity is a mystery for the human mind and it has crept in to mathematics as well. Infinity, as we know, is endless; not an enormous number but a representation of an eternal number.

According to definition of infinity, it's simpler than most things which have a definite beginning and ending because infinity just is and can not be measured. It's use in mathematics has been narrowed down since it can behave like a real number but does not follow the properties of a real number. In fact infinities lie beyond the boundaries of real numbers, - ∞ < x < ∞ where x is a real number.

Some properties that infinity follows are:
∞ + ∞ = ∞
-∞ + -∞ = -∞

∞ × ∞ = ∞
-∞ × -∞ = ∞
-∞ × ∞ = -∞

x + ∞ = ∞
x + (-∞) = -∞
x - ∞ = -∞
x - (-∞) = ∞

x × ∞ = ∞, x > 0
x × (-∞) = -∞, x > 0

x × ∞ = -∞, x < 0
x × (-∞) = ∞, x < 0

Functions never are able to reach infinity, since it's endless, but only reach towards and is known as approaching it's limit.

Problems involving finding limits, as it is well know, is not enjoyable and can mess with one's brain. L'Hopitals's rule attempts to make it easier. The process in l'Hopital's rule involves finding the derivatives of functions which tend to zero or infinity. And generally the derivative of a function is a measurement of it's rate, so it can be assumed that the derivative helps find the rate at which each function in consideration is reaching zero or infinity. When they are being divided, as l'Hopital's rule imposes, the ratio of the rates is being found. At times this rule can cause the problem to go in circles, but with interruptions of the rule the limit can be found.

As much as infinity and bothers us, I believe it's one of the most amazing concepts understood by humans. Because as much as everyone believes in the end of the Universe, I believe the Universe will go on forever and (until we have discovered otherwise) the Big Crunch will not take place.
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By Kowsheek Mahmood
Ryerson University, Toronto, Canada
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The Aftermath Publications, Issue 3
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