Infinity Definition and 988 Threads

Infinity represents something that is boundless or endless, or else something that is larger than any real or natural number. It is often denoted by the infinity symbol shown here.
Since the time of the ancient Greeks, the philosophical nature of infinity was the subject of many discussions among philosophers. In the 17th century, with the introduction of the infinity symbol and the infinitesimal calculus, mathematicians began to work with infinite series and what some mathematicians (including l'Hôpital and Bernoulli) regarded as infinitely small quantities, but infinity continued to be associated with endless processes. As mathematicians struggled with the foundation of calculus, it remained unclear whether infinity could be considered as a number or magnitude and, if so, how this could be done. At the end of the 19th century, Georg Cantor enlarged the mathematical study of infinity by studying infinite sets and infinite numbers, showing that they can be of various sizes. For example, if a line is viewed as the set of all of its points, their infinite number (i.e., the cardinality of the line) is larger than the number of integers. In this usage, infinity is a mathematical concept, and infinite mathematical objects can be studied, manipulated, and used just like any other mathematical object.
The mathematical concept of infinity refines and extends the old philosophical concept, in particular by introducing infinitely many different sizes of infinite sets. Among the axioms of Zermelo–Fraenkel set theory, on which most of modern mathematics can be developed, is the axiom of infinity, which guarantees the existence of infinite sets. The mathematical concept of infinity and the manipulation of infinite sets are used everywhere in mathematics, even in areas such as combinatorics that may seem to have nothing to do with them. For example, Wiles's proof of Fermat's Last Theorem implicitly relies on the existence of very large infinite sets for solving a long-standing problem that is stated in terms of elementary arithmetic.
In physics and cosmology, whether the Universe is infinite is an open question.

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  1. B

    Behaviour of implicit ODE solution as x approaches infinity

    Homework Statement This is the solution to an IVP, and the question asks how the function behaves as x Approaches infinity...
  2. K

    Integration by parts and infinity

    Homework Statement integrate (x*2e^x)/(2e^x-1)2 from x=0 to infinity Homework Equations The Attempt at a Solution let t=2e^x-1 => x=ln((t+1)/2) dt = 2e^x dx Thus equation is now integrate (ln((t+1)/2))/t^2 dt from t=1 to infinity Then let u = (t+1)/2 => 2du=dt Equation now...
  3. L

    Is Infinity Plausible in the Universe?

    Hello. The word "infinity" often comes up in physics, but observational evidence seems to preclude any form of infinity whatsoever: either everything must be infinite, or nothing can be infinite. My line of thought comes from the fact that the density of our universe is not infinite. Therefore...
  4. K

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  5. K

    Is Chemical Knowledge Truly Infinite?

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  6. K

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  7. K

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  8. S

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  9. Y

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  10. K

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  11. M

    The Consequences of Making Infinity a Number in Mathematics

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  12. I

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  13. D

    Infinity corrected lens - expanding before tube lens?

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  14. A

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  15. N

    What is the limit of a^x when a tend to infinity and x tend to 0?

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  16. S

    F uniformly continuous -> finite slope towards infinity

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  17. Z

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  18. C

    Is the Concept of Infinity Misunderstood in Mathematics and Philosophy?

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  19. Fredrik

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  20. R

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  21. F

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  22. Femme_physics

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  23. L

    Bringing 3 Charges from infinity into a triangle

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  24. A

    Work to move charge to infinity?

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  25. A

    Work to move charge to infinity problem

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  26. P

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  27. P

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  28. D

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  29. S

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  30. F

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  31. Y

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    We often have lim_{x\rightarrow a}f(g(x)) = f(lim_{x\rightarrow a} g(x)) if f(x) is continuous at g(a). But then my question arises where g(x)\rightarrow\infty. I am not sure if there is any meaning to continuity at infinity as it seems that continuity is the property of a particular...
  32. A

    Moving Charges to Infinity: Work Required and Comparison

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  33. K

    Question about limits at infinity with radicals.

    Homework Statement Find the following limit: \lim_{x \to \infty} \frac{2+\sqrt{(6x)}}{-2+\sqrt{(3x)}} Homework Equations n/aThe Attempt at a Solution I know this shouldn't be that hard, but somehow I keep getting stuck on simplifying the equation. I think the first step is to multiply both...
  34. B

    Entropy change as mass tends to infinity

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  35. S

    What is the Correct Notation for Infinity when Taking a Limit?

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  36. C

    What Is the Correct Minimum Velocity from Infinity?

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  37. C

    What Is the Correct Approach to Evaluate Limits at Infinity with Square Roots?

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  38. L

    Exploring the Mystery of an Expanding, Infinite Universe

    I'm reading a lot of stuff about the expanding universe, and also about it being infinte. So now I was wondering: How can the universe expand while it's infinte? (or am I asking something that nobody really know's the answer to?)
  39. P

    How to Determine Charge Density on a Plane from a Point Charge?

    Homework Statement hello, the problem is that i have charge q which lies in d distance from a plane and I need to find function \sigma which describes density of this charge The Attempt at a Solution I wrote this situation in cylindrical coordinate system where q lies in point A=(0,0,h) and...
  40. S

    Is infinity plus or minus one possible?

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  41. romsofia

    Is Infinity a Concept or a Number?

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  42. D

    Compute the integral of x^a / (1+x^2) for x going from 0 to + infinity

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  43. A

    Mean tends Infinity in Gaussian Case

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  44. R

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  45. P

    Limits of Infinity: Does f(x) Exist?

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  46. C

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  47. H

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  48. A

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  49. M

    Evaluate the following integral from 0 to infinity

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  50. J

    Sum to infinity of Heaviside function

    I'm revising my course text for my exam and came across a Fourier series problem finding the Fourier series of the square wave: http://img574.imageshack.us/img574/5862/eq1.png. It is then calculated that the complex Fourier coefficients are...
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