They are: - zero divided by zero - infinity divided by infinity - zero times infinity - infinity minus infinity - zero to the zero power - infinity to the zero power - one to the infinite power. This is because any number with zero as its exponent will equal one. There are seven indeterminate forms, of which 0/0 is just the best known. In this case it could be said the answer is 1 because of the zero exponent, but that is assuming that (∞) is a real number; which it is not. As the sequence of values of x become very small numbers, then the sequence of values of y, the reciprocals, become very large numbers.The values of y will become and remain greater, for example, than 10 100000000. y becomes infinite. Any constant raised to the 0th power, other than 0, is 1. In that case, every student from the infinity to the power of infinity students can be assigned to one of the seats, numbered 0, 1, 2, .... To describe how that works, we'll need a way of identfying each student. identifying students Properties of Infinity Addition with Infinity Infinity Plus a Number Infinity Plus Infinity Infinity Minus Infinity Multiplication with Infinity Infinity by a Number Infinity by Infinity Infinity by Zero Division with Infinity and Zero Zero over a Number A Number over Zero A Number over Infinity Infinity over a Number… Similarly, negative infinity to the negative one power (-∞ ^ -1) also approaches zero. However, if not in the context of a limit, infinity raised to the 0th power is undefine since it is only a concept and not a number.-----EDIT: Regarding e, it is more common to put the limit this way, lim .. The meaning of infinity.The definition of 'becomes infinite' Let us see what happens to the values of y as x approaches 0 from the right:. Presume there is some algorithm that makes it possible. Infinity to the power of 0 equals one. Unfortunately, I was not able to prove what zero to the negative one power (0 ^ -1) equals. $\begingroup$ i am assuming from your answer that if a>1 then limit x--> + infinity or - infinity of a to the power x is = 0 $\endgroup$ – Zia ur Rahman Oct 5 '11 at 13:07 2 $\begingroup$ @Zia: No. It looks like from the positive data set (from the table on the right) that zero to the negative one power (0 ^ -1) approaches positive infinity. anything to the power of 0 is 1, so i'd say 1..... *However, infinity (∞) is a concept, not a number, so your question was flawed from the start.
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