If 8^2/8=8 and (8*8)/8 = 8 what do the following equal?
1) infinity^2/infinity
2) (infinity * infinity)/infinity
2006-08-02 09:32:08 · 19 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
First of all, infinity is not a number but a notation.
Secondly, the 2 questions are of indeterminate form. They cannot be solved like variables.
2006-08-04 09:57:23 · answer #1 · answered by Samvit 1 · 0⤊ 0⤋
Well...Thats hard to explain, but both choices are infinity. Because infinity is not a "real" number (because nothing in the universe have infinity of something), the answer may be undefined. But to answer to your answer, it's none of the above (if there's one) because 8 is NOT equal to infinity...
2006-08-02 09:42:46 · answer #2 · answered by Anonymous · 0⤊ 0⤋
1. infinity
2. infinity
No standard mathematical/algebraic expression combining infinity with any other object, including infinity will get you anything *but* infinity with one exception:
infinity^infinity = something greater than infinity
Confused? You should be, math breaks down in the presence of infinities, but we have managed to eek out some properties of this "number". Take a look at here:
http://en.wikipedia.org/wiki/Infinity#Infinity_in_set_theory
2006-08-02 09:41:50 · answer #3 · answered by kain2396 3 · 0⤊ 0⤋
the answer is 1
infinity^2(or infinity*infinity) = infinity as it is impossible to go higher, so infinity/infinity must = 1 (as anything over itself = 1)
well thats what i think
2006-08-02 09:38:09 · answer #4 · answered by justice_is_spoonfed 2 · 0⤊ 0⤋
Read slowly, meditate upon these words of wisdom, and you may become enlightened. Or perhaps confused.
I am aware of two levels of infinity.
A1 The number of counting or natural numbers (1,2,3,4,...)
A2) The number of real numbers (every number on the continuous number line).
You can't match up A1 to A2 in any way where A2 is completely covered. So A2 > A1.
However...(A1) can match up evenly to (A1) x 2, and (A1) ^ 2, and even (A1) ^ n, where n is some known natural number. So, really, you could say that (A1 x A1) is the same as (A1). And so your question above is that Infinity ^2 / Infinity is the same as Inf/Inf, which would equal 1.
Just in case you are wondering, it is safe to say that 2 ^ (A1) is greater than (A1), although I can't be sure as to whether 2 ^ (A1) is the same order as (A2).
2006-08-02 12:03:12 · answer #5 · answered by Polymath 5 · 0⤊ 0⤋
Meaningless, since +- infinity/+- infinity is not defined even when you are working with the extended reals.
2006-08-02 09:40:12 · answer #6 · answered by Minh 6 · 0⤊ 0⤋
infinity
2006-08-02 09:37:20 · answer #7 · answered by Nientech 3 · 0⤊ 0⤋
infinity
2006-08-02 09:37:04 · answer #8 · answered by ♥Loving*Steph♥ 2 · 0⤊ 0⤋
It doesnt matter what you do to infinity, it's always infinity
2006-08-02 10:01:04 · answer #9 · answered by jessica 2 · 0⤊ 0⤋
actually, it's infinity and 1. (infinity * infinity) = infinity first.
2006-08-02 09:38:55 · answer #10 · answered by Alfred Y 3 · 0⤊ 0⤋