Changes

So infinity might arise in statements like these:

So infinity might arise in statements like these:

*<math>\frac{1}{0} = \infty\ \ </math>NO!  This isn't allowed!  Infinity is not a number, and division by zero is illegal!

*<math>\frac{1}{0} = \infty\ \ </math>NO!  This isn't allowed!  Infinity is not a number, and division by zero is illegal!

*<math>\lim_{x\to 0}\frac{1}{x} = \infty\ \ </math>Yes, sort of.  One could say that "the limit is infinite", since that include both positive and negative infinite values.  But to say that the limit is "equal to infinity", one would have to say that this is the limit from the right.  The limit from the left is "minus infinity", that is, unboundedly negative.  This sort of statement, in terms of limits, is what was presumably meant by the incorrect statement above.

*<math>\lim_{x\to 0}\frac{1}{x} = \infty\ \ </math>Yes, sort of.  One could say that "the limit is infinite", since that includes both positive and negative infinite values.  But to say that the limit is "equal to infinity", one would have to say that this is the limit from the right.  The limit from the left is "minus infinity", that is, unboundedly negative.  This sort of statement, in terms of limits, is what was presumably meant by the incorrect statement above.

*<math>\int_0^1\frac{1}{x} = \infty\ \ </math>Infinity has a special meaning for integrals.

*<math>\int_0^1\frac{1}{x} = \infty\ \ </math>Infinity has a special meaning for integrals.

*<math>\|\mathbb{Z}\| = \infty\ \ </math>The cardinality of the integers is infinite.

*<math>\|\mathbb{Z}\| = \infty\ \ </math>The cardinality of the integers is infinite.