Why infinity ^ infinity is undetermined????????

Answer 1

Infinity is a concept, not a number. You can't take a concept and raise it to the power of another concept. It is meaningless.

Answer 2

If you have infinity, raising it to an infinite power is moot at best.
To answer your question more specifically, raising it to any power would not change the answer at all. Infinity to the second, third or forth power would produce the same non ending number that never ends on the number line. Because this is inconsistent with the rules that a number that is not zero is raised to another power, it should have a different number. This is impossible, and the way mathematicians handle this is to say it is undetermined.

Answer 3

Infinity is a concept of not having a boundary, and the use of infinity in mathematics has to be carefully done. In mathematics, it is very important to be able to get a reliable result.

This means that concepts such as infinity must be handled very carefully. This is why when you are studying mathematics, the book often gives you a bizarre definition that seems to be pointless.

Usually, that is because as time went on, mathematicians have found problems with other definitions that led to contradictions, or they have found that this definition allows them more flexibility later on.

Infinite numbers have been studied, and there are actually different sizes of infinity.

And there are "more numbers" between zero and one than if you compare it to the set of numbers {1,2,3 ...}. The most famous proof of this is called the "diagonal proof". This proofs is not very difficult, but the results can be hard to believe!

"Infinite" numbers are called transfinite, and the mathematician who is most famous for his work studying these is Cantor.

I hope this inspires you to look closer at this intriguing area of mathematics.

Answer 4

nobody knows what number infinity it is the highest most infinite number so infinity to the infinity power is also undetermined

Answer 5

infinity cant be defined i.e. infinity is undetermined, so any expression involving infinity obviously cant be determined. Hence infinity^infinity is undetermined.

Answer 6

infinity ^ infinity is undetermined as 0 ^ 0 is undetermined, too!

^_^

Answer 7

Infinity is not a number.

Infinity is a shorthand way of expressing that functions, sequences, series, etc. grow without bound.

You can't use it in standard arithmetic operations.

Answer 8

If infinity is undefined, then infinity^infinity can't be.

Answer 9

infinty is not a real number (undetermined number ) so thje answer of infinty ^ infinty is impossible to solve, that is why it is undetermined