# micromass

Mentor

#### Visitor Messages

Showing Visitor Messages 1 to 10 of 409
1. Y 02:38 AM
Welcome back my friend! Glad to see you around again.
2. Y 01:19 AM
drizzle
Yay! You're green!!
3. Mar5-14 09:27 AM
ltjrpliskin
Microooo, I baked you some cookies... but then i eated it :(
Welcome back! <3
4. Mar3-14 09:47 AM
reenmachine
Why life? Who am I? What is the meaning of life?
5. Mar2-14 07:53 PM
WannabeFeynman
Welcome back! I'm new as a member, but I've long been here and seen that you make many high quality posts.
6. Mar2-14 07:22 PM
SammyS
Welcome back, micro!!!

Long time -- No see.

SammyS
7. Mar2-14 04:38 PM
lisab
*hugs!* Can't chat now, but I'm glad to see you!
8. Mar2-14 04:22 PM
Welcome back micromass :)
9. Mar2-14 02:19 PM
jhae2.718
Welcome back, friend.
10. Mar2-14 02:07 PM
drizzle
Welcome back!!

Country
Belgium
Educational Background
Master's
Degree in
Mathematics
Favorite Area of Science
Biology

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• Last Activity: T 01:42 AM
• Join Date: Oct10-09

#### Friends

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#### Blog

View micromass's BlogRecent Entries
Latest Blog Entry

Posted Aug5-13 at 05:03 PM by micromass Comments 0
Posted in Uncategorized
The newest challenge was the following:

 Prove that ##\mathbb{N}## contains uncountably many subsets ##(N_\alpha)_{\alpha \in \mathbb{R}}## such that ##N_\alpha\cap N_\beta## is finite if ##\alpha\neq \beta##.
This was solved by HS-Scientist. Here's his solution:

 For any $a \in [0.1,1)$, define $S_a=(\lfloor 10a \rfloor,\lfloor 100a \rfloor...,\lfloor 10^na \rfloor...)$. For example, $S_\frac{\pi}{10}=(3,31,314,...) ... Posted Aug3-13 at 03:53 PM by micromass Comments 0 Posted in Uncategorized I have recently posted a challenge in my signature. The challenge read as follows:  Let ##f:[0,+\infty )\rightarrow [0,+\infty )## be a twice differentiable function such that ##f(0) = 0##. Prove that if ##f^{\prime\prime}(x)\leq 0## for all ##x##, then ##f(x+y)\leq f(x) + f(y)## for all ##x## and ##y##. The first answer I got was from Millenial. He gave the following correct solution:  Let [itex]g(x) = f'(x)$. Then, the question
...

Posted Jul8-13 at 06:28 AM by micromass Comments 1
Posted in Uncategorized
If you're not careful with indefinite integration, then paradoxes soon arise. For example, consider the following:

$$\int 0 dx = 0 \int 1dx = 0(x + C) = 0$$

But we also know that the integral of ##0## is supposed to be ##\int 0dx = C##. What's going on?

As another example, consider ##\int \frac{1}{x}dx##. This is an easy to solve integral, but let's apply integration by parts on it, we get

[tex]\int \frac{1}{x} dx = \frac{1}{x} x...

Posted Feb6-12 at 11:24 PM by micromass Comments 14
Posted in Uncategorized
I have not been a mentor for very long, but I can see pretty clearly that we get quite a lot of complaints of people who think the PF-rules are too strict or that we should be more lax in enforcing the rules. It may not surprise any of you that I disagree with this. But let me try to explain my motives behind my disagreement.

First of all, there is only one person in this entire forum who decides what the rules are. That person is Greg. It is his forum. He is the one who spends a...

Posted May25-11 at 04:37 PM by micromass Comments 5
Posted in Uncategorized
Whenever I need to learn a new subject in mathematics, I try to be very careful about which book I learn it from. Usually, I look on the internet and I see what other recommend. Very often, this gives very good results and gives textbooks that are real good. However, there are two books that everybody seems to adore, but which I absolutely hate. The purpose of this blog is a bit to rant about this books.

The first book which I think is far too overrated is the rubbish that...