Infinity

  • Infinity

  • lLammar Academy

    lLammar Academy

    Organizer
    April 24, 2021 at 9:01 am

    Infinity Meaning

    A set of numbers can be defined as infinite if there exists a one-to-one correspondence between that set and a proper subset of itself.

    Let us consider an example x+ 1 = x, this is only possible when x is an infinite number. The addition of 1 won’t result in a change in the original number.

    Another way to represent an infinite number is 1/x when x→0

    The most interesting thing about infinity is – ∞ < x < ∞, which is the mathematical shorthand for the negative infinity which is less than any real number and the positive infinity which is greater than the real number.

    Here, “x” represents the real number.

    Symbol

    The mathematical symbol infinity ” ∞” was discovered by the English mathematician John Wallis in 1657. There are three different types of infinity, namely: mathematical, physical, and metaphysical. The direct use of the infinity symbol in mathematics arises in order to compare the sizes of the sets such as the set of counting numbers, the set of points in the real number and so on.

    The infinity symbol ∞ is sometimes called the lemniscate and is a mathematical symbol representing the concept of infinity. The sign of infinity is used more often to represent a potential infinity, rather than to represent an actually infinite quantity such as the ordinal numbers and cardinal numbers. For instance, in the mathematical notation for summations and limits.

    Properties

    The list of important properties of infinity is given below.

    Addition Property

    If any number is added to infinity, the sum is also equal to infinity.

    ∞ + ∞ = ∞-∞ + -∞ = -∞Multiplication Property

    If a number is multiplied by infinity, then the value of the product is also equal to infinity.

    ∞ × ∞ = ∞-∞ × ∞ = -∞-∞ × -∞ = ∞Some Special Properties

    If x is any integer, then;

    x + (-∞) = -∞x + ∞ = ∞x – (-∞) = ∞x – ∞ = -∞

    For x > 0:

    x × (-∞) = -∞x × ∞ = ∞

    For x < 0:

    x × (-∞) = ∞x × ∞ = -∞Value of Infinity

    However, in mathematics, infinity is the conceptual expression of such a numberless number. It is often treated as if it were a number that counts or measures things: “an infinite number of terms, but it is not the same sort of number as natural or real numbers.

    For example, A list of natural numbers 1, 2, 3, 4,…….no matter how long you count for, it can never reach the end of all numbers. Similarly, the never-ending universe, if you travel in the fastest spaceship, you can’t reach the end of an unending universe.

    Examples

    Go through the list of examples of infinity given below:

    Example 1:

    The sequence of natural numbers. (i.e) {1, 2, 3,4, 5, ….} which is endless. We can say it as an infinite sequence.

    Example 2:

    Consider a fractional number 1/3. When you perform a division operation on this number, we can get the result 0.3333…., where the number “3” is repeated indefinitely.

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