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1234th Post!
PikaPika999   230
N 2 hours ago by Shan3t
I hit my 1234th post! (I think I missed it, I'm kinda late, :oops_sign:)

But here's a puzzle for you all! Try to create the numbers 1 through 25 using the numbers 1, 2, 3, and 4! You are only allowed to use addition, subtraction, multiplication, division, and parenthesis. If you're post #1, try to make 1. If you're post #2, try to make 2. If you're post #3, try to make 3, and so on. If you're a post after 25, then I guess you can try to make numbers greater than 25 but you can use factorials, square roots, and that stuff. Have fun!

1: $(4-3)\cdot(2-1)$
230 replies
PikaPika999
Apr 21, 2025
Shan3t
2 hours ago
What Are The Chances?
IbrahimNadeem   65
N 3 hours ago by peelybonehead
Hello, I'm curious to have honest advice on how far I can make it (by 11th-12th grade-ish);

If I have:

- Started AMC 8 study in 6th grade
- Started AMC 10 study in 7th grade
- Started practicing harder & went from 60 to around 100 on AMC 10 (on practice tests with official conditions)
- Started AMC 12 study in 8th grade
- Currently (fall of 8th grade) getting ~120 on AMC 10/12 & 7-10 while practicing AIME

At this rate, what are the chances of me making the USA(J)MO, for example, by ~11th grade?

Please be completely honest and don't hold back; This can be useful to see if I have the need to practice harder.
65 replies
IbrahimNadeem
Oct 31, 2021
peelybonehead
3 hours ago
9 What is the most important topic in maths competition?
AVIKRIS   49
N 3 hours ago by valisaxieamc
I think arithmetic is the most the most important topic in math competitions.
49 replies
AVIKRIS
Apr 19, 2025
valisaxieamc
3 hours ago
random achievements
Bummer12345   19
N 6 hours ago by MathLoverYeah
What are some random math achievements that you have accomplished but possess no real meaning?

For example, I solved #10 on the 2024 national mathcounts team round, though my team got a 5 Click to reveal hidden text and ended up getting 30-somethingth place
19 replies
Bummer12345
Mar 25, 2025
MathLoverYeah
6 hours ago
The daily problem!
Leeoz   131
N Yesterday at 11:10 PM by Shan3t
Every day, I will try to post a new problem for you all to solve! If you want to post a daily problem, you can! :)

Please hide solutions and answers, hints are fine though! :)

Problems usually get harder throughout the week, so Sunday is the easiest and Saturday is the hardest!

Past Problems!
131 replies
Leeoz
Mar 21, 2025
Shan3t
Yesterday at 11:10 PM
Basic, Part B
CarSa   1
N Yesterday at 10:41 PM by Math-lover1
For each four--digit number $\overline {abcd}$, that is, with $a$ nonzero, let $P(\overline {abcd})$ be the product $(a+b)(a+c)(a+d)(b+c)(b+d)(c+d)$.
For example, $P(2022) = (2+0)(2+2)(2+2)(0+2)(0+2)(2+2) = 512$ and $P(1234) = (1+2)(1+3)(1+4)(2+3)(2+4)(3+4)$.
How many numbers $\overline {abcd}$ with at least one $0$ amoung their digits satisfy that $P(\overline {abcd})$ is a power of 2?
1 reply
CarSa
Apr 24, 2025
Math-lover1
Yesterday at 10:41 PM
random problem i just thought about one day
ceilingfan404   25
N Yesterday at 7:15 PM by maromex
i don't even know if this is solvable
Prove that there are finite/infinite powers of 2 where all the digits are also powers of 2. (For example, $4$ and $128$ are numbers that work, but $64$ and $1024$ don't work.)
25 replies
ceilingfan404
Apr 20, 2025
maromex
Yesterday at 7:15 PM
simplify inequality
ngelyy   14
N Yesterday at 6:39 PM by aoh11
$\frac{24x}{21}+\frac{35x}{49}-\frac{x}{2}$
14 replies
ngelyy
Apr 18, 2025
aoh11
Yesterday at 6:39 PM
300 MAP Goal??
Antoinette14   63
N Yesterday at 5:35 PM by HoneyHap
Hey, so as a 6th grader, my big goal for MAP this spring is to get a 300 (ambitious, i know). I'm currently at a 285 (288 last year though). I'm already taking a intro to counting and probability course (One of my weak points), but is there anything else you recommend I focus on to get a 300?
63 replies
Antoinette14
Jan 30, 2025
HoneyHap
Yesterday at 5:35 PM
Purple Comet Math Meet Recources
RabtejKalra   7
N Yesterday at 3:47 PM by Rice_Farmer
I heard that you can take a packet of information to the Purple Comet examination with some formulas, etc. Does anybody have a copy of a guidebook with all the important formulas? I'm just too lazy to write one myself.......
7 replies
RabtejKalra
Apr 24, 2025
Rice_Farmer
Yesterday at 3:47 PM
Questions about dividing by 0
Arr0w   28
N Nov 15, 2024 by b2025tyx
I have a couple of questions all of which have to do with dividing by 0. Thanks in advance.
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28 replies
Arr0w
Dec 2, 2020
b2025tyx
Nov 15, 2024
Questions about dividing by 0
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Arr0w
2908 posts
#1 • 2 Y
Y by mobro, DDCN_2011
I have a couple of questions all of which have to do with dividing by 0. Thanks in advance.
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This post has been edited 1 time. Last edited by Arr0w, Dec 2, 2020, 5:02 PM
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Math2k06
148 posts
#2 • 3 Y
Y by Mango247, Mango247, Mango247
$1/0$ is not a number.For #3, since anything times $0$ is $0$, the answer should be $0$.

Tldr don't poke into questions including $0$ and division. You will open a parallel univeerse
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aaja3427
1918 posts
#3
Y by
S2

@above that wouldn't be true since you are multiplying by undefined. Anything to do with undefined is undefined.
This post has been edited 1 time. Last edited by aaja3427, Dec 2, 2020, 5:08 PM
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mop
4054 posts
#4
Y by
Undefined numbers are a class of their own. Thus, they cannot be used with real or imaginary numbers without creating an undefined result.
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cubingsoda
19220 posts
#5 • 3 Y
Y by Mango247, Mango247, Mango247
see this video

He divides $a - b$ but since $a=b$ he divides by $0$. He gets $1=2$!

Dividing by $0$ opens the black hole
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correcthorsebatterystaple
620 posts
#6
Y by
Yeah, there are a couple of constructs in higher maths which assign a value to 1/0 (sort of like $i$) but you have to bend the rules of arithmetic a bit and what's going on here (1-3) is definitely not that. They're not that useful, either. We leave 1/0 undefined most of the time, similar to how you would say "no solutions" if you were asked to solve $x^2=-1$ over $\mathbb{R}.$ (to answer 5)

An "undefined value" has no numerical value; I think even calling it a "value" in the first place is a bit of a misnomer.
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ihatemath123
3445 posts
#7
Y by
S4
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cubingsoda
19220 posts
#8
Y by
undefined = no answer so no solution
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SteindorfStrongGirl
116 posts
#9
Y by
i made a presentation on this at school :< its something about 1≠2
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Awesome_Twin1
751 posts
#12
Y by
1. Avoid double posting
2. Don't bump this thread. Just look at A Letter to MSM which has been pinned.
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A_MatheMagician
2251 posts
#13
Y by
please read this post first
sry @above sniped me
This post has been edited 1 time. Last edited by A_MatheMagician, Dec 14, 2023, 1:45 AM
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vrondoS
165 posts
#14
Y by
In some ways, you can think $\frac{1}{0}=\infty$. This isn't rigorous, however, because then $\frac{2}{0}=2\infty=\infty$. Thinking about it this way can help explain some of the questions you had.
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A_MatheMagician
2251 posts
#16
Y by
Post #14 by vrondoS
infinity is not a value
that does not make any sense
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ZekeMath
42 posts
#17
Y by
If it's undefined, eventually somebody will define it :) I say better now than later.
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Yummo
297 posts
#18
Y by
Awesome_Twin1 wrote:
1. Avoid double posting
2. Don't bump this thread. Just look at A Letter to MSM which has been pinned.
A_MatheMagician wrote:
please read this post first
sry @above sniped me

Do you realize who posted that? @Arr0w, I thought you left AoPS a while ago.
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mathboy282
2989 posts
#20
Y by
vrondoS wrote:
In some ways, you can think $\frac{1}{0}=\infty$. This isn't rigorous, however, because then $\frac{2}{0}=2\infty=\infty$. Thinking about it this way can help explain some of the questions you had.

I would argue that this isn't true. $1/0 is undefined.$ The limit of it also does not exist, because:
$\lim_{x->0^+}\frac1x = +\infty$
but also:
$\lim_{x->0^-} \frac1x = -\infty$
This post has been edited 2 times. Last edited by mathboy282, Dec 14, 2023, 3:33 AM
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JoyfulSapling
824 posts
#21
Y by
Arr0w wrote:
I have a couple of questions all of which have to do with dividing by 0. Thanks in advance.
1
2
3
4
5

Solutions:
1
2
3
4
5
This post has been edited 4 times. Last edited by JoyfulSapling, Mar 14, 2024, 2:33 PM
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MathPerson12321
3731 posts
#22
Y by
I would think a variable like b would be defined as $\frac{1}{0}$, similar to $i$.
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the_mathmagician
467 posts
#23
Y by
Note: defining a number like $b=\frac{1}{0}$ serves no purpose. Why did we define $i$? Because we created the quadratic formula and realized that we couldn't describe the full range of solutions. Plus, we found something called casus irreducibilis, in which we found that describing a root of a cubic that was a real number required the use of imaginary numbers. After we accepted that we found a lot of useful other things to do with complex numbers. As for with "$b$", it serves no purpose. What can we do with this? There's nothing we can do with it. Actually, all it does is completely break our current framework of math.

Edit: Also, read this by the OP, written a few years later. It's an announcement but MSM unfortunately isn't known for paying attention to those ;)
This post has been edited 2 times. Last edited by the_mathmagician, Mar 14, 2024, 4:10 AM
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yummy-yum10-2021
95 posts
#24
Y by
Arr0w wrote:
Greetings.

I have seen many posts talking about commonly asked questions, such as finding the value of $0^0$, $\frac{1}{0}$,$\frac{0}{0}$, $\frac{\infty}{\infty}$, why $0.999...=1$ or even expressions of those terms combined as if that would make them defined. I have made this post to answer these questions once and for all, and I politely ask everyone to link this post to threads that are talking about this issue.
[...]
What about $\frac{1}{0}$? Suppose that $x=\frac{1}{0}$. Then we would have $x\cdot 0=0=1$, absurd. A more rigorous treatment of the idea is that $\lim_{x\to0}\frac{1}{x}$ does not exist in the first place, although you will see why in a calculus course. So the point is that $\frac{1}{0}$ is undefined.
[...]
What about $\frac{0}{0}$? Usually this is considered to be an indeterminate form, but I would also wager that this is also undefined.
[...]
INDETERMINATE VS UNDEFINED

What makes something indeterminate? As you can see above, there are many things that are indeterminate. While definitions might vary slightly, it is the consensus that the following definition holds: A mathematical expression is be said to be indeterminate if it is not definitively or precisely determined. So how does this make, say, something like $0/0$ indeterminate? In analysis (the theory behind calculus and beyond), limits involving an algebraic combination of functions in an independent variable may often be evaluated by replacing these functions by their limits. However, if the expression obtained after this substitution does not provide sufficient information to determine the original limit, then the expression is called an indeterminate form. For example, we could say that $0/0$ is an indeterminate form.

But we need to more specific, this is still ambiguous. An indeterminate form is a mathematical expression involving at most two of $0$, $1$ or $\infty$, obtained by applying the algebraic limit theorem (a theorem in analysis, look this up for details) in the process of attempting to determine a limit, which fails to restrict that limit to one specific value or infinity, and thus does not determine the limit being calculated. This is why it is called indeterminate. Some examples of indeterminate forms are
\[0/0, \infty/\infty, \infty-\infty, \infty \times 0\]etc etc. So what makes something undefined? In the broader scope, something being undefined refers to an expression which is not assigned an interpretation or a value. A function is said to be undefined for points outside its domain. For example, the function $f:\mathbb{R}^{+}\cup\{0\}\rightarrow\mathbb{R}$ given by the mapping $x\mapsto \sqrt{x}$ is undefined for $x<0$. On the other hand, $1/0$ is undefined because dividing by $0$ is not defined in arithmetic by definition. In other words, something is undefined when it is not defined in some mathematical context.


Full post: A Letter to MSN
This post has been edited 1 time. Last edited by yummy-yum10-2021, Nov 11, 2024, 3:41 AM
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greenplanet2050
1318 posts
#25
Y by
yummy-yum10-2021 wrote:
Arr0w wrote:
Greetings.

I have seen many posts talking about commonly asked questions, such as finding the value of $0^0$, $\frac{1}{0}$,$\frac{0}{0}$, $\frac{\infty}{\infty}$, why $0.999...=1$ or even expressions of those terms combined as if that would make them defined. I have made this post to answer these questions once and for all, and I politely ask everyone to link this post to threads that are talking about this issue.
[...]
What about $\frac{1}{0}$? Suppose that $x=\frac{1}{0}$. Then we would have $x\cdot 0=0=1$, absurd. A more rigorous treatment of the idea is that $\lim_{x\to0}\frac{1}{x}$ does not exist in the first place, although you will see why in a calculus course. So the point is that $\frac{1}{0}$ is undefined.
[...]
What about $\frac{0}{0}$? Usually this is considered to be an indeterminate form, but I would also wager that this is also undefined.
[...]
INDETERMINATE VS UNDEFINED

What makes something indeterminate? As you can see above, there are many things that are indeterminate. While definitions might vary slightly, it is the consensus that the following definition holds: A mathematical expression is be said to be indeterminate if it is not definitively or precisely determined. So how does this make, say, something like $0/0$ indeterminate? In analysis (the theory behind calculus and beyond), limits involving an algebraic combination of functions in an independent variable may often be evaluated by replacing these functions by their limits. However, if the expression obtained after this substitution does not provide sufficient information to determine the original limit, then the expression is called an indeterminate form. For example, we could say that $0/0$ is an indeterminate form.

But we need to more specific, this is still ambiguous. An indeterminate form is a mathematical expression involving at most two of $0$, $1$ or $\infty$, obtained by applying the algebraic limit theorem (a theorem in analysis, look this up for details) in the process of attempting to determine a limit, which fails to restrict that limit to one specific value or infinity, and thus does not determine the limit being calculated. This is why it is called indeterminate. Some examples of indeterminate forms are
\[0/0, \infty/\infty, \infty-\infty, \infty \times 0\]etc etc. So what makes something undefined? In the broader scope, something being undefined refers to an expression which is not assigned an interpretation or a value. A function is said to be undefined for points outside its domain. For example, the function $f:\mathbb{R}^{+}\cup\{0\}\rightarrow\mathbb{R}$ given by the mapping $x\mapsto \sqrt{x}$ is undefined for $x<0$. On the other hand, $1/0$ is undefined because dividing by $0$ is not defined in arithmetic by definition. In other words, something is undefined when it is not defined in some mathematical context.


Full post: A Letter to MSN
There’s no need to bump this thread.
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vincentwant
1347 posts
#26
Y by
me when the person who posted this is the same person who posted a letter to msm:
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Turtle09
1814 posts
#27
Y by
vincentwant wrote:
me when the person who posted this is the same person who posted a letter to msm:

this is crazy lol
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sadas123
1236 posts
#28
Y by
honestly I think that 1/0 is infinity because if you graph this on a graphing calculator it looks like this and you can see the largest red line is when you divide with 0 and if you do it with a smaller number with 1 which I will also include makes it a very large slope change, which looks like it is going to infinity.
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club52
724 posts
#29
Y by
@above it goes to both positive and negative infinity.
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b2025tyx
1474 posts
#30
Y by
Sol 4
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blimpo
801 posts
#31
Y by
I would like to point out that undefined and infinity are not numbers, but definitions. So you can't say "x is equal to infinity" or "when dividing this by undefined"
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Catcumber
162 posts
#32
Y by
guys stop bumping this thread... its 4 years old
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b2025tyx
1474 posts
#33
Y by
Catcumber wrote:
guys stop bumping this thread... its 4 years old

Whoops, forgot to check that
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