Linked Questions

66
votes
14answers
4k views

Pseudo Proofs that are intuitively reasonable

What are nice "proofs" of true facts that are not really rigorous but give the right answer and still make sense on some level? Personally, I consider them to be guilty pleasures. Here are examples ...
44
votes
7answers
2k views

Bad Fraction Reduction That Actually Works

$$\frac{16}{64}=\frac{1\rlap{/}6}{\rlap{/}64}=\frac{1}{4}$$ This is certainly not a correct technique for reducing fractions to lowest terms, but it happens to work in this case, and I believe there ...
36
votes
6answers
5k views

Geometric explanation of $\sqrt 2 + \sqrt 3 \approx \pi$

Just curious, is there a geometry picture explanation to show that $\sqrt 2 + \sqrt 3 $ is close to $ \pi $?
40
votes
3answers
2k views

Common Math Mistakes Made by Scientists

I am a mathematician by training working with a physicist. I have been invited to give an hour-long tutorial/presentation to incoming graduate students. These students are all coming in with physical ...
11
votes
4answers
942 views

Which step in this process allows me to erroneously conclude that $i = 1$

I was playing around with imaginary numbers and exponents and came up with this: $$ i = \sqrt{-1} $$ $$ \sqrt{-1} = (-1)^{1/2} $$ $$ (-1)^{1/2} = (-1)^{2/4} $$ $$ (-1)^{2/4} = ((-1)^{2})^{1/4} $$...
10
votes
3answers
357 views

What is the limit $\lim_{n\to\infty}\frac{1^n+2^n+3^n+\dots+n^n}{n^{n+1}}$?

I want to determine the limit given below: $$\lim_{n\to\infty}\frac{1^n+2^n+3^n+\ldots+n^n}{n^{n+1}}$$ I have tried to solve thise several times ,but with no results.I have tried using lema stolz ...
0
votes
3answers
6k views

Multiplication using Tangents.

I got a maths problem and just checking whether my answer and method is correct: Tan(A+B/2) / Tan (A-B/2) = SinA + SinB / SinA - SinB I started to solve it: <...
10
votes
2answers
5k views

Proving the equivalency of Principle of Mathematical Induction and Well Ordering Principle

I would like to know how from the very basic I can teach some one the above title statement. Here is my plan. $\textbf{First}$ I will state WOP: Every non-empty set of positive integers contains a ...
2
votes
2answers
2k views

Proof by induction failure if assumption is wrong?

I never got a clear answer to this question in college. What happens in an induction proof if the assumption is wrong? For example, suppose we try to prove that $n^5$ > n! for n >= $2$ so we start ...
8
votes
3answers
197 views

Interesting Differentiation Technique

@HansEngler Left the following response to this question regarding "bad math" that works, Here's another classical freshman calculus example: Find $\frac{d}{dx}x^x$. Alice says "this is ...
3
votes
2answers
271 views

When does L'Hopital's rule pick up asymptotics?

I'm taking a graduate economics course this semester. One of the homework questions asks: Let $$u(c,\theta) = \frac{c^{1-\theta}}{1-\theta}.$$ Show that $\lim_{\theta\to 1} u(c) = \ln(c)$. Hint: ...
16
votes
1answer
652 views

successful absurd formalities

Has anyone published in print or on a web site or elsewhere a compilation of successful illogical formal arguments? By those I mean arguments that follow a form in disregard of the legality of its ...
0
votes
3answers
128 views

Correct Method of finding the limit

Is this the correct way to solve for the limit? I found the limit $x\to 0$ of $\sin4x/ \tan7x$ by these steps 1) $\dfrac{\sin4x}{1} \cdot \dfrac{\cos7x}{\sin7x}$ 2) I crossed out the $\sin x$ in ...
1
vote
1answer
292 views

$\sqrt 2+ \sqrt{3} \approx 3.14$ [duplicate]

The square $$\sqrt 2+ \sqrt{3} \approx 3.14$$ Is this a coincidence or is their some mathemtical significance?
4
votes
2answers
118 views

Inequality for $\sum_{n=1}^\infty \frac{x^n}{n^n}$.

I need to show that for $x<0$, $$\sum_{n=1}^\infty \frac{x^n}{n^n}<0$$ but I am completely stuck. I noted that the series is alternating, the first term is negative, but the term is only ...

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