It looks like you're using an Ad Blocker.
Please white-list or disable AboveTopSecret.com in your ad-blocking tool.
Thank you.
Some features of ATS will be disabled while you continue to use an ad-blocker.
I will have to see some examples of dividing by zero happening all the time, I still stand by that it can't happen.
Originally posted by OutKast Searcher
Originally posted by PhysicsAdept
reply to post by OutKast Searcher
Has to do with rates is my guess. You cannot just multiply each side by infinity to resolve that 1=2.
Ok seriously, last post of the night, more tomorrow
Why not?
So now not only is infinity a number, but it is a number that has different values at different times? And it doesn't follow basic algebra rules?
You hit the nail on the head with your last statement.
Originally posted by jb1958
Hmm, I think I can grasp infinity divided or multiplied by a number, but the OPs question, of 1 divided by infinity, I am struggling with. 1 divided by anything more than zero gives less than 1 right? a fractional number. And 1 divided by infinity? Seems it would be more than zero but less than one of something.
So in your world....100 = 1 and 45 = 0 and 32 = 98???? I'm sorry...but I have to say you are more confused than anyone else in this thread. I would suggest that you take some formal courses instead of just teaching yourself...easy to confuse yourself to the point where valid mathematics will never make sense to the incorrect world view you have built in your mind.
Yes and no.
Originally posted by jb1958
reply to post by saige45
Maybe a good way to visualize this, is we would have an infinite number of parts of something, but since there are an infinite number of them, you could never collect all the parts, so you could never make a whole something out of these parts. So no matter how hard you tried, forever, you have more than zero of it, but can't ever make a whole 1.
lim 1/x = 0 x->∞ limes means that the function gets closer to... (in the case of 1/x) to 0, but does not mean it IS 0.
This has got to be one of the dumbest threads i have ever read.
If zero means none, nothing, nil, then you have none of whatever. zero apples times 3 is still zero apples, I still don't have any. But can infinity be divided or multiplied by zero, what does that mean? An infinite number of apples divided by zero, the zero becomes irrelevant relative to infinity's size, so the answer is still infinite? This is intriguing, what do other members think?
Originally posted by circlemaker
Originally posted by OutKast Searcher
I request a thread be made on "shadow numbers".
Maybe I'll present my counter argument of "invisible numbers".
No need for an entire thread. Count from infinity instead of 0 and you're dealing with shadow numbers. From 0's perspective they're all collapsed to infinity. From infinity's perspective all the numbers which use 0 as their origin are collapsed to 0.
Instead of offering non-answers I actually figure stuff out.
Here's a picture showing shadow numbers next to the "real numbers". The awareness barrier defines the numbers we haven't counted to yet, hence the name.
Originally posted by PhysicsAdept
reply to post by Bob Sholtz
So because ∞-∞ does not =0, you would agree that some ∞s are larger than others?
ETA: also, to be noted, there are an infinite amount of numbers between 2 and ∞, but also 2 and 3.edit on 18-3-2012 by PhysicsAdept because: (no reason given)
Originally posted by ClydeFrog42
reply to post by WhatAreThey
You see, the idea of this process is represented by limits. As this continues on, as we *approach* infinity (as our number gets larger in larger), the answer approaches zero.
You are making the false assumption that infinity is something that can be "approached". As if you keep dividing forever you will hit infinity and zero at the same time....
Signed zero is zero with an associated sign. In ordinary arithmetic, −0 = +0 = 0. However, in computing, some number representations allow for the existence of two zeros, often denoted by −0 (negative zero) and +0 (positive zero). This occurs in the sign and magnitude and ones' complement signed number representations for integers, and in most floating point number representations. The number 0 is usually encoded as +0, but can be represented by either +0 or −0.
The IEEE 754 standard for floating point arithmetic (presently used by most computers and programming languages that support floating point numbers) requires both +0 and −0. The zeroes can be considered as a variant of the extended real number line such that 1/−0 = −∞ and 1/+0 = +∞, division by zero is only undefined for ±0/±0 and ±∞/±∞.
Negatively signed zero echoes the mathematical analysis concept of approaching 0 from below as a one-sided limit, which may be denoted by x → 0−, x → 0−, or x → ↑0. The notation "−0" may be used informally to denote a small negative number that has been rounded to zero. The concept of negative zero also has some theoretical applications in statistical mechanics and other disciplines.
In mathematics, the Riemann sphere (or extended complex plane), named after the 19th century mathematician Bernhard Riemann, is the sphere obtained from the complex plane by adding a point at infinity. The sphere is the geometric representation of the extended complex numbers C ∪ [∞], which consist of the complex numbers together with a symbol ∞ to represent infinity.
The extended complex numbers are useful in complex analysis because they allow for division by zero in some circumstances, in a way that makes expressions such as 1/0 = ∞ well-behaved. For example, any rational function on the complex plane can be extended to a continuous function on the Riemann sphere, with the poles of the rational function mapping to infinity. More generally, any meromorphic function can be thought of as a continuous function whose codomain is the Riemann sphere.
In geometry, the Riemann sphere is the prototypical example of a Riemann surface, and is one of the simplest complex manifolds. In projective geometry, the sphere can be thought of as the complex projective line P1(C), the projective space of all complex lines in C2. As with any compact Riemann surface, the sphere may also be viewed as a projective algebraic curve, making it a fundamental example in algebraic geometry. It also finds utility in other disciplines that depend on analysis and geometry, such as quantum mechanics and other branches of physics.
Georg Friedrich Bernhard Riemann [ˈʁiːman] ( listen) (September 17, 1826 – July 20, 1866) was an influential German mathematician who made lasting contributions to analysis and differential geometry, some of them enabling the later development of general relativity.
In mathematics (specifically in differential geometry and topology), a smooth manifold is a subset of Euclidean space which is locally the graph of a smooth (perhaps vector-valued) function. A more general topological manifold can be described as a topological space that on a small enough scale resembles the Euclidean space of a specific dimension, called the dimension of the manifold. Thus, a line and a circle are one-dimensional manifolds, a plane and sphere (the surface of a ball) are two-dimensional manifolds, and so on into high-dimensional space. More formally, every point of an n-dimensional manifold has a neighborhood homeomorphic to an open subset of the n-dimensional space Rn.