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Applying an operator with respect to a variable
There are seemingly two kinds of “operations” used in mathematics when it comes to working with functions; you can either take a function (...)
October 10, 2013 – Jakub Marian – Mathematics
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How can chaos be deterministic?
Perhaps you have already heard the term “deterministic chaos”. It sounds like an oxymoron, doesn’t it? One would expect chaotic (...)
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Can mathematical theorems be proved with 100% certainty?
Many a mathematician considers mathematics to be the only truly exact science and would like to believe that the answer to the question in (...)
September 9, 2013 – Jakub Marian – Mathematics
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Are scientific theories objective?
Virtually all physicists praise the scientific method as the best possible approach to discovering the laws of nature because it is (...)
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Do natural numbers exist?
Imagine a life form consisting of jelly in water whose only sensation of the outer world is a continuous scale of pressure. It is not (...)
August 29, 2013 – Jakub Marian – Mathematics
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By the way, have you already seen my brand new web app for non-native speakers of English? It's based on reading texts and learning by having all meanings, pronunciations, grammar forms etc. easily accessible. It looks like this:
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Are mathematical objects real?
There are two major (and very different) “world views” among mathematicians. Adherents of Plato’s view believe that mathematical objects (...)
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Intuition behind the Cauchy-Schwarz, Markov’s, and Jensen’s inequality
People often tend to learn inequalities just as formulas that are to be memorized, not to be thought about. There is, however, usually an (...)
March 13, 2013 – Jakub Marian – Mathematics
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Base 60: Digits and terminology
Ideally, every number (in its abstractness) should have its own symbol. However, since there are infinitely many natural numbers and our (...)
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