Simple but confusing
Which of the following is/are true?
(A) ∞ = ∞ (B) 1/∞ =1/∞ (C) +∞ > -∞ (D) ∞/∞ = ∞/∞
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1 solution
But +∞ should be greater than -∞ as +∞ lies on right side and -∞ lies on the left side of origin on the number line, right? Whenever one represents range of a function, say y=x^3, range is represented as y belongs to (-∞,∞). Since while representing range, one writes lowest value first, then highest value achieved by that function, separated by a comma, enclosed in brackets, this should imply -∞ should be less than+∞. Please clear my doubt.
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statement: − ∞ = − ∞ + 1 = − ∞ + 2 = . . = − ∞ + 2 ∞
now we cannot determine − ∞ + 2 ∞ . but i think you get the idea right. you can never do arithmetic with infinity. remember this. you can do if limit is given or it is the upper/lower bound of a sum, improper integral,product etc. hope this helps
while you are right, the defination of infinity is not 0 x . 0 x cannot be defined. l i m n → 0 + n x , is infinity. what you did is the same as ∞ 1 = 0 . please correct the solution.
Infinity is a number that's expressed as 0 x with x being all possible numbers. The equation itself is wrong, so none of those statements are correct.