is known as the indeterminate form. The motivation for this name is that there are no rules for comparing the value of to the other real numbers. Note that, for example, is not indeterminate, since we can justifiably associate it with , which does compare with the rest of the real numbers (in particular, it is defined to be greater than all of them.)
1 Other Indeterminate Forms
Although is often called “the” indeterminate form, there are many others. Some of these are:
, for the same motivating reasons as .
; which is the result of much impassioned debate (especially since is defined to be 1, counter-intuitively, but not unreasonably).
; notably because of the derivation of :
A direct substitution would yield .
|Date of creation||2013-03-22 12:28:19|
|Last modified on||2013-03-22 12:28:19|
|Last modified by||akrowne (2)|