LIMITS
One interesting and not commonly known topic is limit
and infinity. The funny thing is they are both controversial
topics and oppose each other. Infinity deals with limitless
and unending things delving deeper into psychological
and theological theories and focusing on the universe.
Limit is things that have an end or the finishing line.
Limit:
Limit is the value that a function or sequence “approaches”
as the input or index approaches some value.
Think about what would happen if the world did not have
any limits (mathematically I mean). Theoretically derivatives
would not exist and since they don’t exist we would not be
able to find the slope of any cubic or greater exponential
equation. Thus the world is tossed into chaos. �!!! Just
kidding but my point is that limits are very important and
though they seem very small and unknown they assist even
greater problems.
Infinity:
The funny thing is infinity has many sizes. This means that
one set of infinity might not be as great as another set which
creates the fact that there are different sets of infinities out
there and maybe our world’s infinity is not the greatest after
all…
Infinity means number greater than any assignable quantity
or countable number (symbol ∞) and is endless which means
that it does not have an end and that it cannot be measured.
The earliest recording of the word ‚infinity’ was in Greece
from a philosopher named Anaximander who used the word
apaerion to define something limitless. The English origin
comes from the Latin word infinitus which Thun branched
out to infinitas then infinite then finally infinity. The picture
above shows Miletus, an old Greek city now located in Turkey
where Anaximander lived.
Galileo, a famous mathematician, found GALILEO’S PARADOX
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THE CLAPPER 2015 - 2016
which states that since there are gaps between a set of
numbers and a set of squared2 numbers there should be
more natural numbers than squared2 numbers. However,
since every natural number has a squared number then their
sets should be equal.
Like… BOOM!!!! (Mind officially blown)
Infinity and limits are, though we don’t normally see, are
a very interesting part of our daily lives. It is all around!
Well not exactly, but it helps understand technology with
helpful software implications and also the unknown with
theological matters of the universe. Though it doesn’t seem
very important now the principles of infinity have helped
scientists build the basics for what we see today!
Until then, keep exploring the wonderful, yet excruciatingly
hard world of Math.
References:
Mike DeHaan (2011), The Paradox of the Infinite Series
of Square Numbers by Galileo, September 5, 2011
http://www.decodedscience.org/the-paradox-of-theinfinite-series-of-square-numbers-by-galileo/2840
Isaiah OOMMEN
10-A