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Let’s Get Real… Analysis (Part 5): the Monotone Convergence Theorem
It’s time! For long time readers, you might recall that we first mentioned the monotone convergence theorem wayyy back in December of 2024 in the article, “Incredibly Serious, Inductive Sequences“. It’s now time to tackle this once and for all! Oh, and by no…
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Let’s Get Real… Analysis (Part 4): The Squeeze Theorem
We’ve studied what it means for a sequence to converge to a limit, but we don’t want to be forced to have to prove every limit using the definition! So today, we learn our first tool to prove a limit exists and find…
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Let’s Get Real… Analysis (Part 3.2) Uniqueness of Limits
We meet again in our real analysis series! In part 1 we learned about the supremum and infimum and then in part 2 we learned about sequence limits. Part 3 has been broken up into two parts: 3.1 is on the triangle inequality…
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Let’s Get Real… Analysis (Part 3.1) The Triangle Inequality
Let’s get straight into this one today! The Triangle Inequality As the name suggests, this is an equality that can be related back to a triangle. Consider the triangle’s sides below, The triangle inequality states: the sum of any two side lengths of…
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Let’s Get Real… Analysis (Part 2): Sequence Limits
Sequences are absolutely fundamental to real analysis. They are the bed rock of most of what we will learn that will follow. Not only will our work on infinite series be based on taking limits of sequences, but a lot of definitions in…
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Let’s get Real… Analysis (Part 1): Super Supremum and Infamous Infimum
Mathematicians love to generalize/extend ideas and concepts. There seems to be no limit to their creativity in finding ever more generalized versions of everyday concepts. From exponentiation first being shorthand for repeated multiplication, e.g. to extending exponentiation to include rational exponents like And…
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Time Dilation Through the Geometry of Right Triangles
Today’s an exciting day, our first venture into physics together. Since everyone, including myself, loves time dilation and special relativity I really wanted to start with this topic. Also, a small comment one of my friends made regarding how crucial geometry was to…
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Newbie at Number Theory (Part 9): Euler’s Little Theorem
As you might have guessed, we’re going learn about Euler’s generalization of Fermat’s Little Theorem, that I’ve dubbed Euler’s Little Theorem. Note this is only what I call the theorem, unfortunately no one else seems to call it this! But, maybe if you…
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It’s Pi Day!
For the first Pi day after having started akickinthediscovery.com I figured that we should do something special! We’re going to show that the sum of the reciprocals of the squares equals… a surprise alla Euler: a surprise. *******Tangent: We call numbers like square…
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Newbie at Number Theory (Part 8): The Chinese Remainder Theorem
Do you remember when you were asked to solve a system of equations back in algebra class? In the case that you don’t here’s a brief reminder. The goal of these types of questions were to have you find a value of x…
What Comes Next: 1, 2, 4, 8, 16, … hint it’s not 32
Hello,
Welcome to A Kick in the Discovery! If you’re curious where this phrase came from, that’s good! It came from the great physicist Richard Feynman. He was curious about anything and everything and he loved to explain science to others. I want to communicate the same enthusiasm about things that I find amazing! More than that, I want to practice teaching and explaining more and more complex ideas. Communication is very important and very challenging, and I hope this blog helps me learn this skill. With all this said, please bear with me while I practice my writing skills! It will be a process.
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