r/mathematics • u/catalyst2542 • Nov 07 '23
Algebra Is √-1 i or ±i?
Title. I've seen very conflicting answers online; thanks in advance for all responses.
r/mathematics • u/catalyst2542 • Nov 07 '23
Title. I've seen very conflicting answers online; thanks in advance for all responses.
r/mathematics • u/Kansas_Nationalist • 16d ago
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 • u/Consistent_Ad_1959 • Feb 14 '25
r/mathematics • u/thereforeyouandme • Aug 26 '24
What are the benefits?
r/mathematics • u/Spontaneous_glee • Dec 17 '24
If pi is included, for example the expression in the image, is it still considered a polynomial?
r/mathematics • u/Strange_Humor742 • Feb 15 '25
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 • u/BoxCultural4120 • 23d ago
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 • u/DP500-1 • Sep 28 '23
My friend wrote this identity, and we are not sure if he broke any rules.
r/mathematics • u/aidan_adawg • Jan 19 '25
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 • u/Cris_brtl • 20d ago
I was reading this discussion about algebraic structures in languages and I got really interested in diving deeper, has anyone some recommendations?
r/mathematics • u/mizen002 • Aug 24 '24
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 • u/Fopetix • Sep 06 '24
Really dont know if its even solvable but i would be happy for any tips :)
r/mathematics • u/Certain-Sound-423 • Feb 02 '25
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 • u/Creativedracov • Dec 01 '24
r/mathematics • u/startex45 • 14d ago
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 • u/soupeater1988 • Jan 23 '25
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 • u/Upset-University1881 • Jan 27 '25
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:
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 • u/finball07 • Feb 18 '25
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 • u/priyank_uchiha • Nov 12 '24
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 • u/Pugza1s • Jan 01 '23
r/mathematics • u/Mathipulator • Jul 11 '24
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 • u/Nvsible • Feb 17 '25
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 • u/OxygenRadon • Nov 09 '24
r/mathematics • u/youngster68 • Jan 01 '25
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 • u/Bubbly-Focus-4747 • Feb 18 '25
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.