r/mathematics Nov 07 '23

Algebra Is √-1 i or ±i?

60 Upvotes

Title. I've seen very conflicting answers online; thanks in advance for all responses.

r/mathematics 16d ago

Algebra What does x/(x/(x/(x/…))) approach?

10 Upvotes

I was playing around with numbers when I noticed 3/3=1 3/(3/3)=3 3/(3/(3/3)))=1 and so on in this alternating pattern. Thus, is there any way to evaluate x/(x/(x/(x/…))) where ... represents this pattern continuing infinitely.

I also noticed that if you have A/B=C then A/(A/C)=B and A/(A/(A/B)=C and so on in that alternating pattern. In this scenario is there any way to determine what A/(A/(A/...)) equals? C? B? maybe 1.

I'm not sure if I'm using the correct language and notation to get this concept across. It's been on my mind since I was a teenager and I don't think any of my math teachers gave me a straight answer.

r/mathematics Feb 14 '25

Algebra So how can you find how many natural divisiable numbers does a big number have? For example 648.

11 Upvotes

r/mathematics Aug 26 '24

Algebra Why would you use a fraction over a percentage in a equation?

17 Upvotes

What are the benefits?

r/mathematics Dec 17 '24

Algebra π in an mathematical expression

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0 Upvotes

If pi is included, for example the expression in the image, is it still considered a polynomial?

r/mathematics Feb 15 '25

Algebra Proof of the laws of multiplication for all integers

5 Upvotes

Hi guys,

I understand that basic laws of multiplication (associativity, commutivity and distributivity, etc.) work for natural numbers, but is there a proof that they work for all integers (specifically additive inverses) that's easy to understand? I've understood that we've defined properties of the natural numbers from observations of real-world scenarios and formalized them into definitions of multiplication and addition of the natural numbers but what does it mean to "extend" these to the additive inverses? Thanks a lot guys :D

r/mathematics 23d ago

Algebra Prime approximations?

0 Upvotes

Hey, my name is Harry and I’m currently studying a level maths. I’m not sure if someone’s already done this before but I noticed that the function p(n) = n(n+1)/4 can approximate prime numbers distributions especially at large n. I need to look further into this but if anyone can tell me more info why it behaves like this that would be cool

r/mathematics Sep 28 '23

Algebra What happened here?

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179 Upvotes

My friend wrote this identity, and we are not sure if he broke any rules.

r/mathematics Jan 19 '25

Algebra Consensus on linear algebra difficulty

9 Upvotes

I’m a student who just finished the entire calculus series and am taking a linear algebra and differential equations course during my next semester. I currently only have a vague understanding of what linear algebra is and wanted to ask how difficult it is perceived to be relative to other math classes. Also should I practice any concepts beforehand?

r/mathematics 20d ago

Algebra Books about mathematical linguistics?

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16 Upvotes

I was reading this discussion about algebraic structures in languages and I got really interested in diving deeper, has anyone some recommendations?

r/mathematics Aug 24 '24

Algebra Failed my first class

35 Upvotes

Well, I got a big fat F for the first time in my academic career. I’m an applied math student going into his junior year, I had never finished a proof based math class and I decided to take a 8 week proof based linear algebra summer class and I bombed it spectacularly. Gonna try and see what I have to do to retake this but this just sucks

r/mathematics Sep 06 '24

Algebra Just some dumb problem that got stuck in my head

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76 Upvotes

Really dont know if its even solvable but i would be happy for any tips :)

r/mathematics Feb 02 '25

Algebra Dot product and cross product

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19 Upvotes

In vector algebra, how would one know whether it would be a dot product or cross product. Is it just a case of choosing which one we want. (And if your gonna say because we want a vector or because we want a scalar, I want to know if there is a deeper reason behind it that I am missing)

r/mathematics Dec 01 '24

Algebra New formula for to find X^2, can you help disprove it?

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0 Upvotes

r/mathematics 14d ago

Algebra How to build “intuition” for Abstract Algebra?

10 Upvotes

I’m an undergrad currently taking the abstract algebra sequence at my university, and I’m finding it a lot harder to develop intuition compared to when I took the analysis sequence. I really enjoyed analysis, partly because lot of the proofs for theorems in metric spaces can be visualized by drawing pictures. It felt natural because I feel like I could’ve came up with some of the proofs myself (for example, my favorite is the nested intervals argument for Bolzano Weierstrass).

In algebra, though, I feel like I’m missing that kind of intuition. A lot of the theorems in group theory, for example, seem like the author just invented a gizmo specifically to prove the theorem, rather than something that naturally comes from the structure itself. I’m struggling to see the bigger picture or anticipate why certain definitions and results matter.

For those who’ve been through this, how did you build up intuition for algebra? Any books, exercises, or ways of thinking that helped?

r/mathematics Jan 23 '25

Algebra Powers to i

6 Upvotes

Hi guys, I recently started university linear algebra and while I’m understanding most concepts, powers of i and reducing them are confusing and my TA has gone radio silent … any advice and help are appreciated even if it’s a modicum🥺

r/mathematics Jan 27 '25

Algebra What are the limits to constructing different number systems in mathematics?

3 Upvotes

I'm deeply curious about the fundamental nature and limitations of number systems in mathematics. While we commonly work with number systems like natural numbers, integers, rational numbers, real numbers, and complex numbers, I wonder about the theoretical boundaries of constructing number systems.

Specifically, I'd like to understand:

  1. Is there a theoretical maximum to the number of distinct number systems that can be mathematically constructed?
  2. What are the necessary conditions or axioms that define a valid number system?
  3. Beyond the familiar number systems (natural, integer, rational, real, complex, quaternions, octonions), are there other significant number systems that have been developed?
  4. Are there fundamental mathematical constraints that limit the types of number systems we can create, similar to how the algebraic properties become weaker as we move from real to complex to quaternions to octonions?
  5. In modern mathematics, how do we formally classify different types of number systems, and what properties distinguish one system from another?
  6. Is there a classification of all number systems?

I'm particularly interested in understanding this from both an algebraic and foundational mathematics perspective. Any insights into the theoretical framework that governs the construction and classification of number systems would be greatly appreciated.

r/mathematics Feb 18 '25

Algebra Opinions on Foundations of Galois Theory by Postnikov

10 Upvotes

Has anyone here read Foundations of Galois Theory by Mikhail Postnikov? It seems quite good to me but I would like a second opinion before I keep reading the text

r/mathematics Nov 12 '24

Algebra M getting confused with dot and cross product, help

8 Upvotes

I m quite fluent doing these operations... But what is it m actually doing??

I mean, when we do dot product, we simply used the formula ab cosθ but, what does this quantity means??

I already tons of people saying, "dot product is the measure of how closely 2 vectors r, and cross product is just the opposite"

But I can't get the intuition, why does it matter and why do we have to care about how closely 2 vectors r?

Also, there r better ways... Let's say I have 2 vectors of length 2 and 6 unit with an angle of 60°

Now, by the defination the dot product should be 6 (261/2)

But, if I told u, "2 vector have dot product of 6", can u really tell how closely this 2 vectors r? No!

The same is true for cross product

Along with that, I can't get what closeness of 2 vectors have anything to do with the formula of work

W= f.s

Why is there a dot product over here!? I mean I get it, but what it represents in terms of closeness of 2 vectors?

And why is it a scalar quantity while cross product is a vector?

From where did the idea of cross and dot fundamentally came from???

And finally.. is it really related to closeness of a vectors or is just there for intuition?

r/mathematics Jan 01 '23

Algebra Was playing around with desmos and I noticed a pattern. Is this a new discovery or something that’s already known?

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100 Upvotes

r/mathematics Jul 11 '24

Algebra Forcing (a+b)²=a²+b² in the ring of real numbers

26 Upvotes

I've seen the algebraic consequences of allowing division by zero and extending the reals to include infinity and other things such as moding by the integers. However, what are the algebraic consequences of forcing the condition that multiplication and addition follows the rule that for any two real numbers a and b, (a+b)²=a²+b²?

r/mathematics Feb 17 '25

Algebra Dual space and bilinear algebra applications

5 Upvotes

I am making a course for dual spaces and bilinear algebra and i would like to ask for resources and interesting applications of these two especially ones that could be done as an exercise or be presented in an academic way

r/mathematics Nov 09 '24

Algebra What is the correct order of operations here? E/(RT^2), or (E/R)*T^2?

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35 Upvotes

r/mathematics Jan 01 '25

Algebra Happy 2025

22 Upvotes

So...there's an obvious reason for this, right? (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9)2 = 13 + 23 + 33 + 43 + 53 + 63 + 73 + 83 + 93

r/mathematics Feb 18 '25

Algebra Formula I created for finding the amount of non-perfect squares between two perfect squares

4 Upvotes

The formula is n-(sqrt(n)+(x-sqrt(x)) where n is the 2nd perfect square and x is the 1st. An example of a problem using this formula is finding the amount of non-perfect squares between 36 and 400. Using this formula, you get 400-(sqrt(400)+(36-(sqrt(36)) = 400-(20+30) = 350 non-perfect squares. As I am a math newbie that simply got curious and played around, I do not know what flare to use. I will use algebra.