I've often been troubled by this question. There are an infinite number of integers but between every integer, there is an infinite number of rational numbers. Moreover, between each rational number is an infinite number of irrational numbers! So, is the infinite set of integers smaller than the infinite set of irrationals? Also, both sets are subsets of the real numbers. This blows me away...
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There are different degrees of infinity.\nFor instance,\nThere are more real numbers between 0 and 1 than there are natural numbers (1,2,3,4,...)\n\nTry searching for Georg Cantor.\n\nAlso, a countable infinite set is smaller than an uncountable infinite set.  This is what my example is based on.  The set of numbers between 0 and 1 is uncountable.  The natural numbers are countable.
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Devin is wrong .By opposite integers we mean the same natural number with opposite signs.Difference of two numbers is obtained by subtrating one from the other.Hence while subtracting one  number from its opposite,the signs will change and we can never get zero as the result.
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The construction of negative numbers and rational numbers is much more complex than you think. So 3 over -1 is not an arithmetic operation and using the rules of abstract mathematics it can easily be seen it is true.
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the length of an 'interval' is simply the difference of the endpoints of the interval. \n\nlength of (a, b), where a,b are real numbers, is: b-a.\n\nlength of (0, 1) = 1-0 = 1.\n\nlength of (0, 0.5) = 0.5-0 = 0.5.\n\nDifferent lengths, same number of things in both sets (cardinality).\n\nAlso, the number of rational numbers in (0, 1) is infinite but 'countable'. The number of irrational numbers in (0, 1)is infinite but is not countable. This shows that the union of a countable set and an uncountable set is uncountable.\n\nCountable means that we can list the elements of a set like this: \n\n{a, b, c, d, e, ...} or {1, 2, 3, ...,45, 46} \n\nNote that the set can be Infinite or finite.\n\nWe can not list the elements of (0, 1) like this so (0, 1) is not countable.
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Infinity is more of a concept than a number.  I have never seen it used as a number in the problem.\n\nIf you see it as part of a domain, like (5,infinity) it simply means that x can be arbitrarily large, as large as we want it to be (but larger than 5).\n\nInfinity means that there is no limit, no finite value that ends the sequence.  How many numbers are there?  An arbitrary amount, there is no limit.  Hence the "infinite" numbers.
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The real numbers include both rational numbers, such as 42 and −23/129, and irrational numbers, such as pi and the square root of 2; a real number can be given by an infinite decimal representation, such as 2.4871773339…, where the digits continue in some way; the real numbers may be thought of as points on an infinitely long number line.http://en.wikipedia.org/wiki/Real_number\nall real numbers is just ALL of the real numbers\nsomething that is not a real number would be like the square root of -1 http://en.wikipedia.org/wiki/Imaginary_number\nbut don't go too deep into that, because it might confuse you\n\nidentity is when both sides of the equation are EXACTLY the same, so you can't solve it like\n2(4x-6)+3=8x-9\n8x-12+3=8x-9\n8x-9=8x-9 if you try to get rid of the 9 you get 8x\n8x-9+9=8x-9+9\n8x=8x then if you try to get rid of 8x, you get 0\n8x-8x=8x-8x\n0=0\nso, to skip all the unnecessary steps, when you get the EXACTLY\nthe same values on each side of the equation, put identity for the answer
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Numbers never end because for any one we care to name, we can add something infinitely large or small to it to produce still another number which is larger than the first. \n\nSome mathematicians may dispute your assertion that we don't need that many numbers, because what might not be practical today can turn out to be years or centuries down the road.  For example, the development of the concept of infinity ultimately led to the development of the calculus, a powerful tool in just about every advanced and worthwhile endeavor undertaken by man.
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Anything divided by 0 is actually undefined, not infinity or 0. When you think about how that works, it makes sense:\n\nDividing a numerator by smaller numbers makes your number larger. Divide 4 by 2, you get 2. Divide 4 by 1, you get 4. Divide 4 by 0.5, you get 8. And so on until you are dividing by a number so small it's pretty close to 0. The overall number gets larger and goes off into infinity.\n\nBut, if you divide a negative number in the same manner, your number gets smaller. -4 by 2 is -2, -4 by 1 is -4, -4 by 0.5 is -8, etc. As you approach 0, your numbers go off into negative infinity.\n\nYou'll have the same weird effect if you divide by negative numbers - a positive divided by an increasingly smaller negative will yield negative infinity, and a negative divided by an increasingly smaller negative will yield positive infinity.\n\nYou can't have it both ways - dividing by zero yields both a positive and negative infinity! So someone a long time ago decided that since a number can't really have two values, it will be undefined.
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Part of your question says, "...q*0/0...," which is of course irrational. Your question needs revision or clarification of some kind.
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square root of 3 is an irrational number\nirratioal number can't be described as fraction
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no:\nsqrt(2) + (-sqrt(2)) = 0 rational\nno\nsqrt(2)*(1/sqrt(2)) = 1 rational\n\nsqrt(2) and 1/sqrt(2) are irrational\n\n In general , it's more often that sum ( product) of too irrational is irrational
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Infinite? I am not sure if you meant real things like people, sand, etc. or abstract things - but here goes:\n\nthe set of integers\nthe set of even integers\nthe number of numbers (or fractions) between 0 and 1\nthe line\nan infinite loop in computer programming
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Nb2718 and ixat01 have understood the concept well.\n\nYour question has kindled me to refresh my knowledge about numbers.\n\nFirst we shall deal with rational number.\n\nA rational number is in the form P/Q. (P and Q are integers and Q is not equal to zero) \n\nAny rational number is an integer when Q = 1. \n\nDecimals are simply a different way of expressing a rational number.\n\nSquare root of two is an irrational number and hence it cannot be expressed as an irrational number \n\nWhat we can do best is to find a rational number which is more or less equal to that irrational number. \n \nThe number we find can either be written in P/Q form or in decimal form because both represent one and the same.\n\nFor example, the ratio of the circumference of a circle to its radius is an irrational number. \nIf we write 22/7 then it is a rational number.\n If we write 3.1415927, then it is 31415927/10000000. Again it is a rational number. \n\nThen how to represent an irrational number in a simple way? The great mathematicians have guided us.\n\nThe simple way of writing this is Pi. \n\nSimilarly how to write the square root of two?  Write 2^ (1/2).\n\n In fact, the figures 1,2 , 3 etc are all symbols only.\n\nThe multiplication factor 1000000 is written as 10^6 or simply 1M.\n\nIn algebra we use x or y to denote any quantity. Thus there exists many numbers of ways to express any quantity in a simple way.
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I vote for infinity, because when studied one finds out that it is even more puzzling and contradictory than it appears on the surface.\n\nGeorg Cantor, listed in a previous answer, proved some very surprising things about infinity. In fact Cantor's work lead to set theory, which most students have seen to some degree, even in high school.\n\nHere's a few commonly taught items about infinite that Cantor discovered:\n\n+ There are various degrees of infinity, not just one.\n\n+ The two most commonly described degrees of infinity are countably infinite and uncountably infinite. Countably infinite means that all elements in that set map to the set of integers. Uncoutably infinite means that there are even more in that set than there are integers.\n\n+ Rational numbers, i.e., fractions, are countably infinite. That means there's a one-to-one mapping between fractions and integers. (Dove-Tail Proof)\n\n+ Real numbers, i.e., includes all [non-repeating] decimals are uncountably infinite. That means there are more reals than rationals even if both sets are infinite. (Diagonalization Proof)\n\n+ Buy using a set theory technique, the set of infinte sets can be grown to even "larger" sets of infinity. In fact, there's an infinite degree of infinite sets.\n\nCantor also had a hypothesis that there was no set of size in between the basic countable and uncountable degrees of infinity, but he couldn't prove it, and it turns out for good reason. Well after his death, other mathematicians proved that his continuum hypothesis could not be proven nor disproven, but that starts to open up a whole new can of worms.
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Since it is a "little" while, it obviously has a quantitative value, therefore it is not an infinite while.  \n\nWhile I am thinking about it, since it is a "little" while, it is therefore not the biggest or maximum while.\n\nIf we restrict our thinking to big and little whiles, then we can assume that it is at least less than or equal to a while that falls exactly between a big while and a little while, therefore a little while is only at the most half the size of a big while, that is, [ little while <= 1/2 big while ]\n\nNow at least we have limited a little while to the lowest half of possible whiles.\n\nWhile this may seem somewhat of a wily answer at least you can be somewhat assured that while you are contemplating awhile about a while, that it only took a little while because if it had taken a big while then you probably would have gotten bored in a little while and wondered again about the whiles and wherefores of the answer and therefore taken twice as long wondering about the wherefores too. That would have taken quite a while.
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Rational:  it makes sense to divide 0 by another number and get 0\nReal:  0 is a real number\nIrrational:  No, that would be the case if it were 5/0\nInteger:  Any whole positive or negative number, and/or 0 \nWhole:  0 is not fractional\n\nTherefore:  0 is a real, whole, rational integer
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To paraphrase your question, is it possible for π to contain, say, 129 successive 3's but not 130 of them?\n\nIf the digits of π are truly random then it would contain any possible sequence, not only the above special cases. This property of "normality" is conjectured, but not known to be true.\n\nThe website in the Source allows you to find sequences in the first 200 million digits of π. Example: 777777777 occurs, but 7777777777 does not occur in the first 200 million digits of π.