Download Common Math Errors by Dawkins P. PDF
By Dawkins P.
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Extra info for Common Math Errors
A =∞ where a ≠ −∞ ∞+∞ =∞ 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. e. a < 0 ) 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. Subtraction with negative infinity can also be dealt with in an intuitive way.
A really, really large number divided by a number that isn’t too large is still a really, really large number. ∞ =∞ if a > 0 a ∞ if a < 0 = −∞ a −∞ if a > 0 = −∞ a −∞ if a < 0 =∞ a Division of a number by infinity is somewhat intuitive, but there are a couple of subtleties that you need to be aware of. I go into this in more detail in the section about 1 1 Misconceptions about and above, but one way to think of it is the following. A ∞ 0 number that isn’t too large divided by infinity (a really, really large number) is a very, very, very small number.
When you add two non-zero numbers you get a new number. For example, 4 + 7 = 11 . With infinity this is not true. With infinity you have the following. ∞+a =∞ where a ≠ −∞ ∞+∞ =∞ 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. e. a < 0 ) 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.