Abstract
This paper explains that the solution to Stepran's infinity puzzle
is not so difficult and has nothing to do with infinity, although the calculus of this equation may in fact be infinite. The author underscores that the puzzle is not a puzzle at all and is not indicative of infinity but rather is purely an exercise in the limitations of physics. The paper agrees with Rucker's concept of infinity as simply a natural element of the universe or of being one of the basic functional elements of mathematical device. The author concludes that the useful concept of infinity is that it does naturally occupy points in both physical and mathematical space ,which truly cements it within the context of a tangible mathematical and physics principle rather than some far-off rationale construct created and identifiable only by mathematical theorists.

Table of Contents:
The Puzzle
The Solution
Response Page to Postings
Discussion

From the Paper
"Stepran's states that a person is tasked with turning a light switch off and on starting with on at 2 minutes and then in increments by half of the time remaining flipping the switch to the opposite position. On the surface the outcome appears as if it will be a simple persuasion of the ineluctable quality of time; that, time is unavoidable and all things must come to an end. Yet, as one begins the calculations it becomes apparent that the half increments are, apparently, infinite starting with two in terms of seconds: 120, 60, 30, 15, 7.5, 3.75, 1.875, .93, .46, .23, .117, .058, .029, ad infinitum, at least to the extent that a common calculator is capable of dividing."

Tags:limitations, solution, natural, continuum, switch

Abstract
This paper focuses on Stepran's puzzle, explaining that this puzzle provides an excellent method to explore the character of infinity relative to tangible outcomes. The paper asserts that Stepran's states that a person is tasked with turning a light switch off and on starting with on at 2 minutes and then in increments by half of the time remaining flipping the switch to the opposite position.

Tags:equation, mathematics, switch

Abstract
This three page undergraduate paper examines an infinity puzzle called 'Doing Business with the Devil'. The writer explains that resolving the puzzle requires accepting the interpretation that there may be many infinities. The writer discusses that if this is true, turning a light switch on and off at ever decreasing intervals and then determining whether the light would be on or off after two minutes would result in a conclusion that the light would be both on and off.

From the Paper
"In discussing and analyzing the "Doing Business with the Devil" puzzle presented in the lecture, resolving the puzzle requires accepting the interpretation that there may be many infinities. If this is true, turning a light switch on and off at ever decreasing intervals and then determining whether the light would be on or off after two minutes would result in a conclusion that the light would be both on and off. From the point of view of Rucker, this is the only logical conclusion that can be made, "for the infinite regresses resulting from recursion" confirm that the infinite "is a real, rather than imagined, concept" (Rucker)."

Tags:infinity, and, perception

Abstract
The 'Doing Business with the Devil' puzzle presents us with a situation in which there are a finite number of one-dollar bills, and the writer is doing business with the Devil, who in this scenario is an avid bill collector. The Devil wants to buy the writer's one-dollar bill with the serial number of 001, and invites the writer to name the price. Some time later he returns and makes a similar offer for the 002 bill. A shorter time later he returns and wants the 003 bill.

From the Paper
"The "Doing Business with the Devil" puzzle presents us with a situation in which there are a finite number of one-dollar bills, and I am doing business with the Devil, who in this scenario is an avid bill collector. The Devil wants to buy my one-dollar bill with the serial number of 001, and invites me to name my price. Some time later he returns and makes me a similar offer for the 002 bill. A shorter time later he returns and wants the 003 bill. This continues indefinitely, while I attempt to amass a fortune."

Tags:infinity, devil, rucker

Abstract
This paper describes the goals and objectives of a series of conferences between the Vatican and leading scientists on questions of Infinity. The paper examines the theological issues involved Infinity.

From the Paper
"The Vatican has historically grappled with resolving the theological issues that are associated with new scientific discoveries. Recently the Vatican press office announced a new project on science and..."

Tags:Vatica, Roman Catholic CHurch, science, Infinity

Abstract
This paper defines infinity and finite. The author describes how humans use cognitive processes to understand the finite with the infinite. The paper relates three types of infinity and how these can be broken down to understand infinity.'

From the Paper
'Is infinity real or is it imagined? How does a finite mind deal with the infinite? Consider the universe and how infinite it. Consider God and how infinite he is. Was there a universe before God? Did time even exist before the Creator? While these are infinite, but things people do are finite such as breathing. Considering whether infinite is real, it is important to look at time, space, and any intervals of these which can be divided or even subdivided and how infinite our minds are. It is important to understand how the finite is quite different than infinite.'

Tags:infinite, finite, mathematics

Abstract
This essay discusses whether infinity can be seen as a real entity. R. Rucker argues that it is quite possible that time may continue forever. Lakoff and Nunez argue that mathematics is the result of the human mind creating metaphors for phenomena it encounters.

Abstract
This paper looks at a couple of Articles on capital structure:"Do Managers have Capital Structure Targets?" by Vikas Mehrotra, Wayne Mikkelson and Megan Partchand, and "The Capital Structure Puzzle," by Michael Barclay and Clifford Smith. The author explains that the main contribution of the first paper is that it provides evidence that managers use the tradeoff theory in selecting a target capital structure. Regarding the second paper, the author explains that the conclusions drawn by the authors are that firms do aim for a desired capital structure, since they make decisions based on the costs of adjusting the capital structure versus the cost of deviating from it.

From the Paper
"Barclay and Smith find that of the three variables, information costs have the weakest relationship with leverage. From this they draw the conclusion that the pecking order theory does not in general hold. They also find that taxes play a role to some extent, based on a finding that 5-10% of the average firm's value is attributable to tax savings from debt. Lastly they also find that contracting costs has a strong relationship with leverage. As the growth opportunities increased the amount of leverage decreased."

Tags:business, management, growth

Abstract
This paper looks at Gamow's book and how the storytelling format with which the author and mathematics instructor, George Gamow, approaches his subject and grabs the interest of the reader goes far beyond math, science, physics, and mere numbers placed in esoteric formulae.

From the Paper
"Gamow did indeed "strive" during his life and career - and in One Two Three...Infinity - to "emphasize" the importance of science and technology. He also strove to In his original Preface, written in 1947 at the time the book was first published, Gamow acknowledges that he did not "attempt to tell the whole story" of modern science; he also shows his ability to understand and be modest when he writes (vi) that he has restricted himself to "a general account of physical facts and events in the world of planets, stars, and nebulae..." "

Tags:maths, physics

Abstract
This essay will look at this debate in the context of the puzzle, "Doing Business with Devil," and will explore the debate through the points of view of R. Rucker's Infinity and the Mind and G. Lakoff and R. Nunez's Where Mathematics Comes From.