https://miguelperez.me/tags/math/ Recent content in Math on Miguels Blog https://miguelperez.me/images/papermod-cover.png https://miguelperez.me/images/papermod-cover.png Hugo en-us Wed, 29 Apr 2026 16:27:04 +0100 https://miguelperez.me/posts/limits/ Wed, 29 Apr 2026 16:27:04 +0100 https://miguelperez.me/posts/limits/ <h1 id="limits-exact-value-or-an-approximation">Limits: Exact Value or an Approximation?</h1> <p>Probably the majority of people will say that the limit is an exact construct and not an approximation but instead a unique real number. For the sake of simplicity we will keep it in the real number domain and use polynomials as examples. And indeed, this statement is correct. But books and intuitive explanations always talk about arbitrarily close etc. But arbitrarily close still is not exactly at the point right? It is just arbitrarily close ¯\_(ツ)_/¯<br> We will try to convince even the biggest skeptic (me) that the limit is indeed an exact number and not just an approximation. For this, it might make sense to look at the derivative formula as it is intuitively relatively clear and makes up for great insights.</p>