THE LIFE OF PI AND OTHER INFINITIES:
A Response
Editor's Note: A Packer student studying Advanced Pre-calculus read and wrote a response to a New York Times article which discussed the existence of infinity. The original article can be viewed here.
The possibility of infinity has always been fascinating. In philosophy, infinity can be basically explained and legitimized, as it is simply taking an extremely large amount and adding one more, and then one more, and then one more, and so on to it.
However, when infinity is applied to mathematics, the idea becomes less certain, but the concept of infinity has been generally accepted in things such as Pi and calculus. The idea of dividing by infinity, however, is problematic, as in the case of whether x+∞, x-∞, x∞, x/∞, where x is any real number, as many mathematicians believe that ∞ is an idea, not a real number. However, as we learned earlier in the year, x(infinitely large positive integer) is ∞, since when a number is continuously being increased, either by multiplication or addition, the resulting number is essentially infinity.
The concept of infinity becomes most interesting and uncertain when applied to cosmology. It is almost universally accepted among cosmologists that the universe is expanding, but the idea that the universe is expanding to an infinitely large size is not commonly agreed on. While the more common theory is that the universe will continue to expand for an infinite amount of time and into an infinite amount of space, some cosmologists have theorized that there is, in fact, a limit to how far the universe can expand, and as soon as that limit is reached the universe will retract into itself. The second theory, which would be more likely to be supported by Aristotle, as he “believed in finite space and infinite time,” as Dr. A.W. Moore is quoted as saying, and the second theory gives a limit on space without creating a limit on time. However, with Albert Einstein’s theory of relativity and the idea of space-time, the idea of both infinite space and time is brought back as possible.
However, when infinity is applied to mathematics, the idea becomes less certain, but the concept of infinity has been generally accepted in things such as Pi and calculus. The idea of dividing by infinity, however, is problematic, as in the case of whether x+∞, x-∞, x∞, x/∞, where x is any real number, as many mathematicians believe that ∞ is an idea, not a real number. However, as we learned earlier in the year, x(infinitely large positive integer) is ∞, since when a number is continuously being increased, either by multiplication or addition, the resulting number is essentially infinity.
The concept of infinity becomes most interesting and uncertain when applied to cosmology. It is almost universally accepted among cosmologists that the universe is expanding, but the idea that the universe is expanding to an infinitely large size is not commonly agreed on. While the more common theory is that the universe will continue to expand for an infinite amount of time and into an infinite amount of space, some cosmologists have theorized that there is, in fact, a limit to how far the universe can expand, and as soon as that limit is reached the universe will retract into itself. The second theory, which would be more likely to be supported by Aristotle, as he “believed in finite space and infinite time,” as Dr. A.W. Moore is quoted as saying, and the second theory gives a limit on space without creating a limit on time. However, with Albert Einstein’s theory of relativity and the idea of space-time, the idea of both infinite space and time is brought back as possible.
