What is the relationship between zero and infinity and can one exist without the other?
444442
The only relationship between infinity and zero is Chuck Norris. Chuck Norris has counted to infinity - TWICE! And, zero is the number of people who can kill Chuck Norris.
190303
well if X + Y = zero \nand you become Z\nthen X + Z = infinity\nwhat is wrong with that?
1092455
Yes.  Infinity goes in both directions.  Space is space, large or small.  IMHO  ;-)
7873
well in the demostrantion of the Real numbers...\n\nall the numbers and relations depend of the existence of 1... suck that there are some rules..\n\nso we even demostrate that 1 exists... and that 1 > 0... after that we can prove the existence of any other Real number..
827218
Mathematics wouldn't be as advanced as it is today without the zero. This is because you may have noticed that 0 is very 'powerful' meaning that if for example i had the following expression:\n\n999999x8575x75238x652938x753928x7539042x34173x0\n\nthe answer would be 0. \nIt is this type of number that helps in simplifying alot of equations in calculus. Believe me, without the number 0, planes would not have been to fly!
923907
infinity isnt a set number.  nothing.
62352
t can be any from negative infinity to positive infinity.  It doesn't matter because the 0 in the numerator makes this equation zero, ALWAYS.  The only thing t cannot be is 0, since the denominator cannot be zero.  That would make the equation "undefined."\nWas that your question?
106499
This is the case\ncircumferences no where centres everywhere\n\nJust try,  even you can not imagine NOTHING, because before imagining that, your mind was already there, thereby the NOTHINGNESS is voilated.\n Even the 'ZERO' is not the one we usually think.\nIt is a compromising point of  +(Plus) and - (Minus) infinity !!!!!. Even mathametically all is filled in 'ZERO'. Enven any number, say 100, it is 0-1000, that is to say you have borrowed it from 'ZERO'\nIt enough for now,  there is musch more to say about 'ZERO'
1109681
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.
457166
This is a Frequently Asked Question. Following is my previous answer:\n\nThis question may be asked so frequently (along with the infamous 0.999...) because no concrete axioms or definitions are ever given for the real number system until one studies higher algebra or real analysis; it is assumed that everyone knows what a real number is until then. The proliferation of these questions show that this assumption is no good.\nFor the sake of conciseness, I will not define what a real number is here, as only the algebraic structure of the real numbers is necessary to answer this question. The algebraic structure of the real numbers is what we call a field. A field is an algebraic structure that follows a finite set of axioms. These axioms define what statements are true and false in this system based on the laws of logic. You can find the field axioms here: http://mathworld.wolfram.com/Field.html .\nEach line is preceded by "For all real numbers a, b and c, the following is true...". Note that the proper form of the additive identity and multiplicative identity is that it prescribes the existence of some number 1 and some number 0 such that the equations hold. These same numbers are then used to prescribe the existence of additive and multiplicative inverses.\nDivision a/b is just shorthand for a*(b^(-1)). So in your question, you are looking for 1*0^(-1). It is easy to show that there is no such number as 0^(-1) in any field. Suppose 0^(-1) exists.\nThen 0*0^(-1) = 1. But multiplying both sides by 0^(-1) gives 0 = 0^(-1), which means 0*0 = 0 = 1. This is obviously false.\nSuppose 0 = 1. 0*a = a for all numbers a. But 0*a = (1 + (-1))*a = a + (-a) = 0. Thus 0 is not equivalent to 1 and our sole assumption that 0^(-1) exists must be false. Thus the expression 1*0^(-1) is undefined in a field.\nProof by contradiction is very powerful for many types of statements.\nAs to the limit argument, note that you are evaluating a limit of the function f(x) = 1/x. As we approach 0 from the negative x-axis, this limit decreases without bound, but as we approach 0 along the positive x-axis, the limit increases without bound. Thus, the limit of f(x) at 0 does not exist, so f(0) remains undefined with no continuous way to complete it. The limit is not indeterminate for this function; it does not exist.\nWhile 1/0 is not defined in any number system, |1/0| is defined as positive infinity in extended number systems (which are not fields by the above argument) for various purposes. See http://mathworld.wolfram.com/AffinelyExtendedRealNumbers.html .
924189
Maybe.  But the question is hypothetical -- infinity is a mathematical concept, and does not exist in the real world.
81372
I don't mean to be rude, but none of the above answers are quite right, and some are actually quite wrong. 0/0 is not undefined, 0/0 is not always infinity, 0/0 never means "nothing" (in fact, it is used quite frequently in calculus), and although there is no general way to define 0/0, it most certainly can be defined given enough information in a problem.\n\nNormlparker had it closest, when discussing the nature of division. In other words, 10/2 means take 10 things and divide them into 2 equal groups; when you do, each of those groups will contain 5 things, so 10/2=5. Dividing by 0 doesn't conceptually make sense. You can't take 10 things and divide them into no groups. That answer is UNDEFINED. (Captial letters for vocabulary emphasis, not because I am yelling.)\n\nNow dividing 0 by 0 is a different issue, because you can surely take no things and make them into no groups. However, what's the size of those nonexistent groups? It's not infinity, nor is it undefined, as some previous posters have said. Dividing 0 by 0 is an INDETERMINATE value, and it's exactly as you said--it could equal just about anything.\n\nTake for instance the fraction (x^2+2x-3)/(x-1). If you plug x=1 into the fraction, you get 0/0, but the function is definitely not infinity when you get close to x=1. If you factor the numerator, the fraction becomes [(x+3)(x-1)]/(x-1). Cancel those common factors and you get x+3. In other words, this fraction (although undefined at x=1) gets very close to x+3=1+3=4. In this case, 0/0 is basically 4.\n\nTo be specific, a non-zero number divided by 0 approaches infinity (or negative infinity), but 0/0 can approach lots of things. However, ANYTHING divided by 0 is not a real number. \n\nWhen you took your equation (0)(0)=0 and divided both sides by one of the 0s on the left side, you actually violated a mathematical principle. Sure you can divide both sides of an equation by any number, as long as you are certain that number is not 0.\n\nSome of the most famous mathematical fallacies are based upon divideng by 0 in a sneaky way. You can prove lots of untrue things (such as 1=2) if you do that, and it's actually kind of fun. I used to do that once a year in my geometry classes to "prove" to my students all math was worthless, and as soon as they got excited, I showed them how I fooled them. They usually didn't care so much, but nerds like me think that kind of stuff is hilarious.\n\nHere are some other indeterminate values that can equal anything: (0)(infinity), 1^(infinity), (infinity)/(infinity).
721127
it's the same as infinity plus infinity infinity times, of course.  ;)\n\nnot to be confused with infinity minus infinity infinity times, which would be the opposite.\n\nalso not to be confused with infinity divided by infinity infinity times, which would be a positive number as close to zero as possible w/o reaching zero.
407128
1^infinity = infinity\n1/1^infinity = 0\nthere 1/0 = 1 ^infinity\n THATS IT , I AM TURNING TO BE A GENIUS
281372
No.\n\n\nUPDATE:\n\nSome of your here don't understand the concept of infinity. You don't ever reach, approach or ever come near infinity. A googleplex raised to the power of a googleplex is as far away from infinity as is the number 1. There is also an infinity between any two numbers. For instance, there's an infinity between the numbers 1 and 2, and so on and so on.
667109
Neither of them are real in the normal sense of the word.\nThey are both abstract ideas for concepts we innately understand. One is the concept we understand to represent the cardinality of a lone object. Zero is the concept of the cardinality of the empty set.\n\nThere are symbols for 0 and 1 that we can use in arithmetic manipulations, but 0 and 1 are not real objects.\n\nKind of similar to "red" you can have a red car, a red barn, a red light, but you can't have a red, it doesn't exist except as a description of something else.\n\nMathematically, both are real since the real numbers are and extension of the rationals which are an extension of the integers and zero and one are both integers.
462144
1 is it's own reciprocal.  0 has no reciprocal because it is impossible to divide by 0.