Deanna L. answered • 06/18/14
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Electrical engineering major and music lover with MIT degree
Dalia,
Anything that divides by zero, zero over zero, or infinity over infinity is indeterminate so in this case that's a,d, and e.
Suneil P.
Just a note on the above comment: 0/0, ∞/∞, 0 × ∞, ∞ − ∞, 00, 1∞ and ∞0 are indeterminate forms, among others.
Anything that divides by 0 is not generally considered indeterminate (other than 0/0) but rather undefined. "The reasoning behind leaving division by zero undefined is as follows. Division is the inverse of multiplication.
If a/b=c, then b*c=a. But if b=0 , then any multiple of b is also 0 , and so if a≠ 0 , no such c exists. On the other hand, if a and b are both zero, then every real number c satisfies b*c=a . Either way, it is impossible to assign a particular real
number to the quotient when the divisor is zero.
In calculus, 0/0 is sometimes used as a symbol, and is called an indeterminate form, but the symbol does not represent division in the sense the word is used in ordinary arithmetic.
Another common operation that is undefined is that of raising zero to the zero power. On the one hand, if x\ne 0 , then x^{0}=1. On the other hand, if y is any positive number, 0^{y}=0 , while if y is negative, 0^y implies division by zero, which is undefined. Thus, to make the laws of exponents work in every case where exponents are defined, 0^0 is left undefined."
In calculus, 0/0 is sometimes used as a symbol, and is called an indeterminate form, but the symbol does not represent division in the sense the word is used in ordinary arithmetic.
Another common operation that is undefined is that of raising zero to the zero power. On the one hand, if x\ne 0 , then x^{0}=1. On the other hand, if y is any positive number, 0^{y}=0 , while if y is negative, 0^y implies division by zero, which is undefined. Thus, to make the laws of exponents work in every case where exponents are defined, 0^0 is left undefined."
In contrast "In calculus and other branches of mathematical analysis, limits involving algebraic operations are often performed by replacing subexpressions by their limits; if the expression obtained after this substitution does not give enough information
to determine the original limit, it is known as an indeterminate form."
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Please see
http://en.wikipedia.org/wiki/Undefined_(mathematics).
http://en.wikipedia.org/wiki/Indeterminate_form.
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07/01/14
Dalia S.
06/19/14