Types of Infinity

Types of Infinity - Types of Infinity Most students have...

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Types of Infinity Most students have run across infinity at some point in time prior to a calculus class. However, when they have dealt with it, it was just a symbol used to represent a really, really large positive or really, really large negative number and that was the extent of it. Once they get into a calculus class students are asked to do some basic algebra with infinity and this is where they get into trouble. Infinity is NOT a number and for the most part doesn’t behave like a number. However, despite that we’ll think of infinity in this section as a really, really, really large number that is so large there isn’t another number larger than it. This is not correct of course, but may help with the discussion in this section. Note as well that everything that we’ll be discussing in this section applies only to real numbers. If you move into complex numbers for instance things can and do change. So, let’s start thinking about addition with infinity. When you add two non-zero numbers you get a new number. For example, . With infinity this is not true. With infinity you have the following. In other words, a really, really large positive number ( ) plus any positive number, regardless of the size, is still a really, really large positive number. Likewise, you can add a negative number ( i.e. ) to a really, really large positive number and stay really, really large and positive. So, addition involving infinity can be dealt with in an intuitive way if you’re careful. Note as well that the a must NOT be negative infinity. If it is, there are some serious issues that we need to deal with as we’ll see in a bit. Subtraction with negative infinity can also be dealt with in an intuitive way in most cases as well. A really, really large negative number minus any positive number, regardless of its size, is still a really, really large negative number. Subtracting a negative number ( i.e. ) from a really, really large negative number will still be a really, really large negative number. Or,
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Again, a must not be negative infinity to avoid some potentially serious difficulties. Multiplication can be dealt with fairly intuitively as well. A really, really large
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Types of Infinity - Types of Infinity Most students have...

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