The answer is "10^negative infinite" since "1 x" effectively cancels itself out of the expression. The answer to the expression "10^negative infinite" is not definable. Since the value of the exponent cannot be defined as either odd or even then the answer to the above expression could be either positive or negative. The answer cannot be less than |1| or else you would never get a value above 1. In fact, with an answer of less than |1| you would ultimately approach a zero value but never reach it. With an answer of exactly |1| the end result could be 1 or -1 depending on whether the exponent was originally odd or even which cannot be determined. So the answer would have to be greater than |1|, but if it was anything greater than |1| than that wouldn't work either because you would ultimately pass up the value of 10 by infinite fold. For these reasons the above expression is undefined. I think I got my logic right on this. I was using absolute value signs everywhere since the answer could be a +/- answer depending on the value of the exponent. Am I right on this?

Right on the cancelling out, and I guess you were right on your logic, although you weren't addressing my question. I was trying to express my figure in scientific notation, 1 x 10^-infinite, and the above quote is exactly what it is. It almost approaches a zero value, but never reaches because of the infinite regress. Now back to my original question, try to imagine this in physical terms, can you do it? --Haite

Some right, some wrong. The sign of the exponent has nothing to do with the sign of the final product. You are confusing it with the sign of the base, which is 10 in this case. If the 10 were negative, then it would matter whether the exponent was odd or even. You are right when you say the 1 is irrelevant, since anything multiplied by 1 equals itself. A negative exponent simply means you place the exponential term in the denominator. The answer is 10^negative infinity, which is the same as 1 divided by 10^positive infinity. 10^positive infinity is just infinity. A number divided by infinity is, by definition, equal to zero. So, in the end, the answer is zero.

Stop assailing my question with postulates and corrolaries, let me try and rephrase. I don't think my unit can be expressed mathematically, however I'll try verbally. Think of 0.1, then divide this by 10, and that by 10, ad infinitum. Can you imagine this physically? Now vote people! --Haite

I suppose in a philosophical context you could say this. It is technically true. For simplicity, though, mathematicians just define 1 divided by infinity to be zero, and they are correct in a very real sense. A number approaching infinite smallness will behave like zero, mathematically speaking. If you've had some pre-calculus, you've done limits. This is the same as the limit of the function 1/x, as x approaches infinity. The answer is zero. And to address your philosophical question: The human brain, which is finite, cannot conceive of infinity in any sense other than an abstract concept. This is true not only for infinite largeness, but infinite smallness as well. (Sometimes I even amaze myself.)

ow...ow...OW! DON'T MAKE ME LOCK DOWN THIS THREAD!!!! oowwwwww...that yelling made my brain hurt I've been up since 5:00am

Now another philosophical question, cow's a guy, but that defies the definition of a cow. Please enlighten me. --Haite

The answer is 0. Because the exponent is infinity, you must take the limit to evaluate it. limit of 1/10^infinity is 0

well, I was having a bagel at the time. Cheddar on a bagel before 10am is, well, kind of nasty. thus, the answer remains cream cheese

what about butter? Acctually I can't make out any difference between cheese and butter. But I know ice cream.

The world "bagel" is often used as a synonym for zero, therefore zero = bagel. 1/infinity is also equal to zero. So, by the transitive property of mathematics, 1/infinity = bagel Cream cheese is the only thing that belongs on a bagel before 10 AM. Thus, as Oni has pointed out, the answer is cream cheese. (At least before 10 AM).

Butter is the milk solids seperated out from the whey and churned. Cheese is milk with a coagulant added, like rennet.