r/askmath

So, the set <0,1> contains the same amount of (rational) numbers as the set <1, →&gt;. However, the set <1,2> is exactly as big as the set <0,1>. It is also obvious that the set <1, →&gt; is bigger than the set <1,2> yet they're by this logic the exact same size. Am I going wrong somewhere in my logic? Please help me understand.

Edit: Thanks everyone, I see where I went wrong, I assumed infinity to behave sort of like a number.

An exam question I faced asked if U was a valid subspace if U was the set of polynomials p(x) such that p(5) = 5, x is real. My proof used the fact that a subspace must contain a vector -v such that v + -v = 0v. Let g(x) = v and h(x) = -v.

Then g(x) + h(x) = 0v. Set x = 5

g(5) + h(5) = 0v.

5 + 5 = 0v.

10 = 0v

Is this valid?

My concerns are -

1.) Do subspaces have to contain a -v for every v to be valid?
2.) Is adding 5 +5 = 10 a valid operation if we haven't defined scalar+scalar addition, only that fields are closed under scalar addition in this way.

I am aware I should have used the 0(x) property in this proof

I just had a test where we were supposed to calculate the number of possible (implied natural) numbers with 6 digits that add up to 12. I solved it like:

10⁶=x (cause that calculates absolutely all numbers with 6 digits I think)

X-10%=y(because 10% of them have 0 at the start, I think)

Y-53/54 (because the biggest six digit number adds up to 54 and so there's like 53 other addition numbers possible things other than 12)

And that was my final result. I am really bad at math but everyone in my class is and the test was more of a "try and figure it out" rather than "I taught you this formula in class".

The teacher got 90 by his calculations, I can't remember the process,I got 16650, other classmates got other results and I (shamefully) asked chatgpt and got a different answer. Couldn't understand the explication. Was I even close to the right answer or? English isn't my first language and I am not in any way used to using mathematical terms. (I hope I used the right tag)

It's already proven that there are more real numbers between 0 and 1 than there are natural numbers, but I'm confused about something

If a number can extend infinitely far in both directions from the decimal point, what's stopping us from, say, reversing the order of the digits so that every real number corresponds to the natural number that is that real number backwards? The tenths place of the real number becomes the ones place of the natural number, the hundredths place becomes the tens, and so on and so forth. Under this system, wouldn't we be able to map every real number 0<R<1 one-to-one with a natural number?

Just a few questions from a ninth-grader, about central tendency and spread

1. The program I'm using to learn math tells me that to find the variance, we divide the result of the sigma notation (\sum_{i=1}^{n}(x_{i}-x̄)^{2}) (paste that into desmos or some other equation displayer) by (n - 1) instead of by n for a more "reliable" result. Why does subtracting 1 from n make it a more reliable answer? I cannot think of any justification for subtracting 1 from n here.
2. To find the variance/standard deviation, we can't take the average of the distances between the values and the mean, since that just averages out to 0. But... why do we square (x_i - x̄) in the variance formula instead of just using the absolute value of (x_i - x̄)?? Would that not result in the average distance from the mean?
3. Why are the mean, median, and mode called measures of central tendency? Tendency, according to Merriam-Webster, is a "direction or approach toward a place, object, effect, or limit," which seems as though "central tendency" would mean the spread, not the center. The only possible solution I can think of is that these are the measures of which values the data in the list tends towards, but that just doesn't seem to fit very well.

Hello all please can someone break down and maybe provide math resource links so i can understand how i am getting the answer 25.

I know how to do that math to get the answer but i just do not understand why I get the answer.

If you’re interested in what I’m mathing it how many luminaries or lux are required in a given space.

You would have a maintenance rating of 0.5 to 1 and use the lux requirement to work out how many luminaires are needed.

Edit: Thank you all for using fantastic examples you have made me realise I have literally forgotten my primary school maths. I enjoyed the pizza analogies they were very enjoyable.

I am now going to find some resources to brush up the basics.

14, I have an exam in about 2 weeks, and i realized i am completely helpless.

For reference, my teacher is probably one of the worst teachers i have ever had, she just skims through and does not explain/put analogies or anything like that, ask for help? 50/50 she will not help you, and if she did.. its barely considered an effort.

I would like to add on the increasing use of AI, i myself am guilty, but i like to ask the AI to tear the answer to its smallest pieces, how the answer was generated, formulas, etc.

So, what do i need to know for the basics? I am starting completely from scratch here. My answer is; i just need to know everything i need to know. The basics, nothing niche here.. im talking angles, formulas, the pythareogoem theorem! Whatever it is. Just tell me, my teacher could not do it.. give advice. I really want to learn math, after years of coping by thinking i am stupid. I will not rely on teachers anymore, every year, these math teachers, whether general or specialized.. (i have algebra next year) have failed me. I cannot WAIT to see what the reccomendations are.

https://preview.redd.it/2rm8l4zzob2h1.png?width=310&format=png&auto=webp&s=b39efb0be0bd93ee5676f47300a9ce267e42a916

i was trying to find the sum of a harmonic series (i will have to make n tend to infinity) ,I wanted to know if this was possible without expanding the g.p., also i found kind of a recursion for each element to be raised to a power

https://preview.redd.it/2t5j9w4kpb2h1.png?width=1200&format=png&auto=webp&s=8533b031d2f331ed9e3a01be53e5107432386474

https://preview.redd.it/hmtbtdunpb2h1.png?width=1600&format=png&auto=webp&s=8b123b9acd3b69afbd082044ac1157fd06a7629a

i feel like it is kinda useless tho

Hi community!

After, studying for several months Game Theory with the goal of improve my chances of winning all the games and take decision in real life I struggle to apply theory in real world situation. I mean with the fact that some problems are NP-hard make it almost imposible to apply it instantly in new real world situation. In those cases, I end up relyng on my taste for making decision lol.

So, does anyone have better insights on it?

With the rise of ai/agent systems, its became very hard and important question to evaluate these systems, can we create a mathmatical framework that can evaluate any system given Task, i don't know how to do this , i have some hypothesis, Let say any System S is built using n subcomponent systems, which can be dependent or independent of each other,

What we say when we mean evaluation E of system S is what are the chances this system will fail P(S will fail), if we know this probability and if its less than some threshold t then we usually say this system is good,
Now S is built using n subcomponents ( S1, S2,...Sn)
Lets define a random variable X= S will fail
X= U{k=1 to n} Sk

P(X)= inclusion exclusion principle over Sk=> we need to know 2^n probabilities to be sure

Is my reasoning correct?
Can someone eval this?

This is feel is the most important question of this century!

I've got four points of data and I know the pattern that would create the next points, but I'm trying to remember the process for turning it into a properly written out function. I haven't had a math class in eleven years and I just want to remember how this works lol.

So the four points I have are at (1, 90), (2, 50), (3, 30), and (4, 20). The pattern is that each y value is half of the previous y value plus 5. Remind me of the process to figure out the function that creates this graph? I am so far detached from algebra due to non use that I don't even remember where to begin, I've been spitballing ideas around and I've at least recognized that there's a power of x greater than one involved as well as an inverse function, right? But then, a power greater than one would mean the value of y would begin to grow eventually and it never does from what I can see, it has an asymptote close to y = 10

So I'm new to this whole thing and I'm trying to find how to calculate an arithmetic sum with an odd number of terms. From what I know if the number of terms are even you can do [(a_{1} + a_{n})*n]/2 with n being the number of terms. If the number of terms are odd can we do {[(a_{1} + a_{n})*(n-1)]/2}+a_{b}}, b = [(n-1)/2]+1?

Sorry if the notation is a mess, I'm on mobile

I was thinking about how we define a meter as a fixed distance. If I take that 'meter' and wrap it around a circle to measure an angle,the angle changes depending on the size of the circle.

But if I use 'radians', the angle stays the same while the distance changes.

Which one is the 'real' constant in nature the distance or the angle of it just a scaling ratio.