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What is infinity divided by infinity? - Mathematics Stack Exchange I know that $\infty \infty$ is not generally defined However, if we have 2 equal infinities divided by each other, would it be 1? if we have an infinity divided by another half-as-big infinity, for
Types of infinity - Mathematics Stack Exchange I understand that there are different types of infinity: one can (even intuitively) understand that the infinity of the reals is different from the infinity of the natural numbers Or that the infi
One divided by Infinity? - Mathematics Stack Exchange Similarly, the reals and the complex numbers each exclude infinity, so arithmetic isn't defined for it You can extend those sets to include infinity - but then you have to extend the definition of the arithmetic operators, to cope with that extended set And then, you need to start thinking about arithmetic differently
Can I subtract infinity from infinity? - Mathematics Stack Exchange Can this interpretation ("subtract one infinity from another infinite quantity, that is twice large as the previous infinity") help us with things like limn→∞(1 + x n)n, lim n → ∞ (1 + x n) n, or is it just a parlor trick for a much easier kind of limit?
Ideal points and the line at infinity - Mathematics Stack Exchange Ideal points and the line at infinity Homogeneous vectors x = (x1,x2,x3)T x = (x 1, x 2, x 3) T such that x3 ≠ 0 x 3 ≠ 0 correspond to finite points in R2 R 2 One may augment R2 R 2 by adding points with last coordinate x3 = 0 x 3 = 0 The resulting space is the set of all homogeneous 3 3 -vectors, namely the projective space P2 P 2
complex analysis - Infinity plus Infinity - Mathematics Stack Exchange You'll need to complete a few actions and gain 15 reputation points before being able to upvote Upvoting indicates when questions and answers are useful What's reputation and how do I get it? Instead, you can save this post to reference later
Can infinity be divided by anything? - Mathematics Stack Exchange Since you are talking about "dividing by infinity" then you are probably working in the extended real numbers rather than the real numbers In such a context, yes infinity is the "largest" extended real number and 11 11 can indeed be divided by it
I have learned that 1 0 is infinity, why isnt it minus infinity? This obviously makes no sense - we say that 0 0 is "undefined" because there isn't really an answer Likewise, 1 0 is not really infinity Infinity isn't actually a number, it's more of a concept If you think about how division is often described in schools, say, number of sweets shared between number of people, you see the confusion
Mathematical definition of infinity - Mathematics Stack Exchange Another way "infinity" is used is to describe the size of sets There are an infinite number of integers, and also an infinite number of even integers, and also an infinite number of prime integers, not to mention rational numbers (fractions), or even the set of all polynomials