Jordyn Fernandez
Professor Petersen
Math 101
6 April 2016
To Infinity and Beyond
When one thinks of the word infinity they automatically think never ending or eternal.
But, when one thinks about infinity, they think about their definition of the word and that only.
They do not think about what infinity is used for in terms of math. Infinity is not just a word to
describe a lot. There is history and applications behind the word infinity in terms of math that no
one probably even thinks about. Infinity is endless. It is the idea of something that has no end at
all.
The term infinity has history behind it going back all the way to the early Greeks. As
early as 490 BCE, one of the earliest attestable accounts of mathematical infinity came from a
Greek philosopher by the name of Zeno of Elea. In Greek’s study of matter, they had asked the
question, “can one continue to divide matter into smaller and smaller pieces or will one reach a
tiny piece which cannot be divided further?” (Infinity). Then there was Pythagoras who had
“argued that ‘all is number’ and his universe was made up of finite natural numbers” (Infinity).
Then the Atomists “believed that matter was composed of an infinite number of indivisibles”
(Infinity). Parmenides and the Eleatic School, which included Zeno, had argued against the
Atomists. “However Zeno's paradoxes show that both the belief that matter is continuously
divisible and the belief in an atomic theory both led to apparent contradictions”
(Infinity). Aristotle did not appreciate the significance of Zeno's arguments but the infinite did
worry him at all (Infinity). “Aristotle argued against the actual infinite and, in its place, he
considered the potential infinite” (Infinity). Many years later, in the 17th century, European
mathematicians started to use infinite numbers in a more precise fashion. John Wallis was the
first to use the infinity symbol, which looks like a sideways 8, for “infinite numbers”. Wallis ”
exploited it in area calculations by dividing the region into infinitesimal strips of width on the
order of
” (Infinity, Wikipedia). After Wallis first used the symbol, Euler is the symbol of i
for an infinite number. Euler exploited that “by applying the binomial formula to the i^th power”
(Infinity, Wikipedia). Ever since Wallis had co-invented the symbol for infinity, it is used in
many ways and not just math. It is used in calculus, real analysis, set, theory, and in physics.
A set of numbers is simply endless. Yes, we all think that infinity means that things go on
and on and keep growing, but to make it more simple, saying that it is endless makes more sense.
For example the set of {1, 2, 3, 4…} is endless. Infinity can also be used when measuring a
slope/line on a graph. A line in a graph can be endless. Isaac Newton and Gottfried Wilhelm
Leibniz had introduced the use of infinity to calculus in the late 1600s. “Newton introduced his
own theory of infinitely small numbers, or infinitesimals, to justify the calculation of derivatives,
or slopes” (Infinity Mathematics). To find the slope of a line that is touching a curve at a certain
point, Newton found it helpful to look at the ratio that is between dy and dx. “Dy is an
infinitesimal change in y produced by moving an infinitesimal amount dx from x” (Infinity
Mathematics). But, this theory that Newton had introduced was being criticized for quite some
time. Until this theory of infinitesimal numbers gained “firm footing”, it was redeveloped by a
mathematician named Abraham Robinson in the 1960s.
When counted a set of natural numbers, the set never ends. A natural number is a nonnegative number or a whole number. So, when counting a set of whole numbers and all the
whole numbers, it never ends. It is an endless set of whole numbers. Also, a decimal can be
endless. For example, 1/3 comes out to be 0.3333… It is 0.3 repeating infinitely. People may ask
what happens if it ends in another number, but simply, the 3s will not end. It is an endless
decimal of 3s.
Infinity is much more than just an adjective. It is a powerful word in math and science. It
is dated all the way back to ancient Greeks. Infinity is an endless amount. When people think
about the word infinity, they do not think about the work that was put into infinity. It is not just a
word. There were many people who had created applications and the history of infinity, such as
Greek philosophers Zeno, Aristotle, and Pythagoras. Then there were European mathematicians
such as Euler and Newton. These mathematicians and philosophers created the use of infinity to
find the measurement of a slope or a line have simply created whole numbers to be infinite.
Numbers do not grow, they are endless.
Works Cited
"Infinity." Infinity. N.p., n.d. Web. 30 Mar. 2016.
Rucker, Rudy. "Infinity." Encyclopedia Britannica Online. Encyclopedia Britannica, n.d. Web.
23 Mar. 2016.
"What Is Infinity?" What Is Infinity? N.p., n.d. Web. 23 Mar. 2016.
Wikipedia. Wikimedia Foundation, n.d. Web. 23 Mar. 2016.