Are there as many real numbers as there are integers?
340469
The amount of real numbers AND the amount of integers are both infinite.  Therefore, I there are an infinite number of integers and an infinite number of real numbers, so the answer to your question would be YES.  (Both are infinite) \nAnother way to look at it, however, is between the numbers 1 and 2 (2 consecutive integers) there can be an infinite amount of real numbers.  In this light you one might argue that there are more real numbers than integers.
795285
first of all, you need to know that there are basically two types of numbers. Real and imaginary. \nreal numbers are those which can be represented in one form or another, but they exist in real world. for example, if you say that there are 4 trees, that means that you can count the number of trees to be a distinct value, ie., 4.\nor consider this. the probability of an event happening is 0.58. this means that the event will be successful 58 times if it is performed 100 times. \nreal numbers consist of all the rational, irrational numbers. that means all these can be realised to be present.\n\nnow coming to imaginary numbers, these are not actually present. \nconsider a number like sqrt(-1). we all know that a square root of a negative number doesnt exist. so, we just say that sqrt(-1) doesnt exist. such numbers can be conveniently represented as Imaginary Numbers. these numbers donot mean anything in the real world, but help in our mathematical calculations.\nnow, hope this answers your question....
157677
This question cannnot be answered due to a simple fact that there are infinite amounts of numbers, therefore is no limit to a higher or a lower number.
19510
It is not true for all a and b. It is true if and only if a and b are positive real numbers.
44369
There is an infinite quantity of numbers between 5/8 and 1/4
980349
Domain:  all real numbers\nRange:  [2, positive infinity]   (all real numbers from 2 to positive infinity)
711526
well, an integer is a whole number (postive or negative) or zero.\nsuch as 37463, or -2, or 0.
758845
NO!\nThe cardinality of the integers the same as that for the rational numbers for instance.  Denoted aleph (א)-null, this "infinity" is "countable", i.e., it can be put in a 1-1 correspondence (bijection) with the natural numbers.\n\nThe cardinality of the real numbers is higher.( א-one *) the number of real numbers cannot be put into a 1-1 correspondence with the natural numbers.\n\nThe number of possible curves in a plane is even higher (א)-two\nETC.......(ad infinitum - no pun intended)\n\nWhat is strange here is that the number of odd natural numbers is the same as the number of all natural numbers, even though the former is a subset of the latter!  That is because a bijection exists between the two sets.\nFor example, let every natural number x be associated with the number 2x-1.   The pairings are:\n1 - 1\n2 - 3\n3 - 5\n4 - 7\n5 - 9\netc.\nEvery natural number is paired with every odd natural number.  Thus the sets have the same cardinality.\nNo bijection exists between these countable sets and say, the real numbers however.  In fact, if you pick ANY two numbers, no matter HOW CLOSE TOGETHER, there are still more real numbers between them than all rational numbers combined. The proof of this is rather cumbersome for here, I suggest you read up on Georg Cantor or infinite sets elsewhere\n\n*It is my "choice" to accept as convention (one side or another of) the continuum hypothesis - it doesnt really matter, but as one answerer pointed out the real numbers' cardinality usually represented as 'c' (Although I never liked that designation-too easily misinterpreted as something else.  I can try to sway supporters, cant I?)
844343
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.
29898
Well it depends on what you want to define as a "number". Since you have already included imaginary and complex numbers, I might suggest you look at Hamilton's quaternions, which are noncommutative, and the nonassociative Cayley numbers, as well as Cantor's transfinite numbers. \n\nOf course, if we follow Leopold Kronecker, we might ignore everything except the integers:\n\n"God created the integers," wrote mathematician Leopold Kronecker, "All the rest is the work of Man."
767112
Here's what you should think: 3 times a number that has to be zero or higher, then having another 3 added to it, cannot possibly equal 1 (it must be at least 3).  So there is no solution.\n\nYou did say it was an inequality, though.  If the = was really > or >=, the answer is all real numbers.  If it was < or <= the answer is the empty set.
55179
hold on let me look at that for a minute....(dya hate math like this as much as i do?)\n\n(1,4) is one for sure\nyea thats' the only one!!!
525085
There is not last number of numbers. In the binary system, or for any system for that matter, you could always add digits to it and the number would increase by at LEAST a power of 10.\n\nInfinity could be the last number, but contrary to popular belief, it is not a number, rather a term stating that something has no end
69389
actually teh biggest number is infinity, and it isnt a defined value, it just embodies very very large numbers, therefore infinity and infinity^2 are actually the same number...pretty neat huh\n\nhope this helps!!
71038
Looks like the first 4 answerers have a good imagination but know nothing about countable sets\n\nSpecifically:\n\n> if you take the real number system,\nit extends from -infinity to +infinity.\n\nLOL, how does that answer the question?\n\n> I think it's uncountable. Yeah, definitely.\n\nOh, are you sure? I mean, really, really sure?\nHow about a reason?\n\n> Uncountable. because between any two real numbers there are infinite number of real numbers.\n\nSo what? Infinite can be countable or not.\n\n> however if u think they are countable, give it a try\n\nLOL, really?\nLet me see you count all natural numbers then (which ARE countable)\n\n> The set of real numbers is uncountable as it contains all the positive natural numbers and the natural numbers are uncountable.\n\nThe natural numbers ARE countable by definition!!!!!\nDo you even know what countable means?!\n\n\n\nOk, let me give a serious answer now.\nThe set of real numbers is uncountable. It was proven by Cantor, in at least two ways.\nThe proofs are not simple enough to be copied here, so I'll just refer you to them.\n\nHis first argument: http://en.wikipedia.org/wiki/Cantor%27s_first_uncountability_proof\nHis diagonal argument (best known): http://en.wikipedia.org/wiki/Cantor%27s_diagonal_argument\n\nRead these pages and follow the proofs.
1052440
The trivial zeros are at (-2K+0i), where K is a positive integer. The nontrivial zeros are all the others. It has been shown that the nontrivial zeroes must have a real part between 0 and 1.
57970
does 1+1=2 is actually a really good question because there is really no way of proving it. Because numbers are abstract(they are not real) they represent other things. But if you look at the equation 1+1=2 you will actually see that by itself it makes no sense because one plus one does not equal a two symbol. so without subsituiting the number symbols for actual things the equation is irrational and cannot be proven.