Difference between revisions of "User talk:Ddk001"
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==Talk== | ==Talk== | ||
Hi! You can say anything here. Please include who is talking. ~[[Ddk001]] | Hi! You can say anything here. Please include who is talking. ~[[Ddk001]] | ||
| + | ==Things I think is interesting== | ||
| + | The purpose of aops is to "Train today's mind for tomorrow's problems". I will now prove that this is impossible. | ||
| + | |||
| + | Suppose, for the sake of contradiction, that "Train today's mind for tomorrow's problems" is possible. Since we have problems today (Day 1), the base case is taken care of. Now, assume that we have problems on Day <math>k</math>. Then, since we are training today's mind for tomorrow's problems, there will be problems on the next day, Day <math>k+1</math>. Hence, by [[induction]], there will be problems every day. This would imply there is infinitely many problems, a contradiction. Hence, the assumption, "Train today's mind for tomorrows problems", is incorrect. | ||
| + | |||
==See also== | ==See also== | ||
* My [[User:Ddk001|user page]] | * My [[User:Ddk001|user page]] | ||
Revision as of 19:07, 15 January 2024
![[asy]draw((0,0)----(0,6));draw((0,-3)----(-3,3));draw((3,0)----(-3,6));draw((6,-6)----(-6,3));draw((6,0)----(-6,0));[/asy]](http://latex.artofproblemsolving.com/d/6/1/d61604256e9de426afc94111a204811ff9d3cf0e.png)
Contents
Problems
Solutions
If you have solved the problems in my user page, put your solution here. We might have a discussion about the solution, like we will on a forum.
Meanwhile, try to do this:
New Problems
If you have a problem to contribute, please put it here. I might add it to my user page. If I have a set of 
good problems, we can consider starting a mock AIME or we can perhaps get the problems into future AIME.
- Note: I am talking mostly of AIME because my problems are all AIME based. If you have AMC or olympiad problems to contribute, you are welcomed to put it here.
Weird expressions
Here is the contest where you try to come up with the with the weirdest expression. Here a record to break:
![\[x=\frac{(19203+\sqrt{\frac{\frac{(\frac{\sqrt[3]{\frac{\frac{\frac{3}{4}}{\frac{4}{3}}}{\pi}}}{\sqrt{10101010}}+121\pi)^{23}}{1902\pi+10} \cdot (\frac{\sqrt[20202023]{\frac{\frac{\frac{3243234}{4234}}{\frac{1023}{323}}}{23\pi}}}{\sqrt{1230}}+23189\sqrt{2}+29384)^{12}}{192019\sqrt{\frac{232}{2093}}+29384\pi}})^{10}}{1029\sqrt{23}+92483\pi+121212}\]](http://latex.artofproblemsolving.com/1/8/1/181cc007b6f8d711b56ad2eeee1638cd0be5655b.png)
~Be sure to include the owner of the expression. If you thought of another one, do not delete the existing ones. Simply add the new one.
Talk
Hi! You can say anything here. Please include who is talking. ~Ddk001
Things I think is interesting
The purpose of aops is to "Train today's mind for tomorrow's problems". I will now prove that this is impossible.
Suppose, for the sake of contradiction, that "Train today's mind for tomorrow's problems" is possible. Since we have problems today (Day 1), the base case is taken care of. Now, assume that we have problems on Day 
. Then, since we are training today's mind for tomorrow's problems, there will be problems on the next day, Day 
. Hence, by induction, there will be problems every day. This would imply there is infinitely many problems, a contradiction. Hence, the assumption, "Train today's mind for tomorrows problems", is incorrect.
See also
- My user page
