Mathematics

If a/b is greater than 1 than b/a must greater than 0 but less than 1.<br><br> For every number greater than 1 there is a multiplicative inverse greater than 0 but less than 1. <br><br> Examples 3/4-4/3, 7/8-8/7, 9/10-10/9, 1/3-3/1, 3/5-5/3 <br><br> But is there a proof for this?<br><br>

Pie value continuation

I couldn't help but wonder if anyone knows how raising e to the imaginary pi power could result in a negative number. In this case, -1. https://en.wikipedia.org/wiki/Euler's_identity Different values of pi can result in different numbers, like 2pi would give a positive one. Then it seems that raising e by a multiple of imaginary pi powers can result in a positive or negative answer. For example, you wouldn't ever be able to raise 1 to an imaginary pi power to ever get a negative answer. You would always just get a positive one. How is e so much more special than 1 to where it's imaginary pi powers can be negative. Then you can raise 2 to an imaginary power…

So one of my pet peeves back when I was into image editing is that in trying to stack images of different aspect ratios vertically such that they'd have the same width; or juxtapose them horizontally such that they'd have the same height; it was always a long, drawn-out game of guess and check to get it right, or at least close enough to right that I could crop it from there. (For the record, I'm referring to Cracked.com, where the combined width in question had to be equal to or fewer than 550 pixels, and the combined height equal to or fewer than 750, rather than outright shrinking one down to and only down to the width or height of the other. Cracked.com is no longer d…

This shows something that appears to be a contradiction in ZF: https://arweave.net/RJ4DRuRjdVWqJ5RBHB30SXDBXATzqmAV3Qs1b6f1ykw (Note that by set-definition I mean it's numeric code, in an encoding such as Godel's encoding.) What the heck? What's wrong? --- It seems I understood why the error: S is a function in a model of ZF, not in the formal system the proof is written. So, it's illegal to use it in the proof. That's a very beautiful sophism. What happens if we try to define S inside ZF? It should fail (unless ZF is contradictory). But how does it fails? That is an practically useful question, because I …

Not even sure how to begin with something " imaginary" and build insight through questions on this, " seriously." From my book on Elementary And Intermediate Algebra, page 584. Talks about the ideas behind the use of a number that is a square root of -1 also referred to as i Uhmmm, Ok.....So then " where did complex numbers come from then?? The page goes onto to mention how negative numbers do not have negative squared roots... Understood, however then it says: Larger number systems that contain the " real number systems" " Real number - Wikipedia" is designed so that negative numbers do have squared roots. Ok....…

I could use recommendations for self study intended to revise a maths unit where I did poorly. General topic is Introductory Calculus and Linear Algebra. The rest of this post is simply detail as to where I am and where I hope to go - so skip if bored. I completed precalculus with flying colours but fell apart in MTHS120 Calculus and Linear Algebra 1. I think I am actually fine (with a little revision) on the basics of integration, differentiation and matrix algebra. Worryingly my issue seems to have been at a deeper conceptual level. I am not permitted to repeat a unit that I actually passed but I have pretty much a whole trimester with no formal study later this ye…

Cracked it in 5 seconds. If you don't know what Kryptos is, read this. CIA website This is so funny. There's no coded messages there!!! Kryptos

For example I asked around the proof of for 1 + 1 = 2 or mathematical proof for any addition and people mentioned different mathematicians for the proof. What is like the standard that is used as the foundation of mathematics. I took high school math but that is about it, I know from a little reading that there are axioms which I think are the foundation of math. Is there a place where these axioms are collected into one?

Good Basic mathematics or Pre-algebra books were hard to find Then i found some good materials here , Pre-Algebra https://www.math-only-math.com/ Algebra https://nios.ac.in/online-course-material/secondary-courses/Mathematics-(211)-Syllabus.aspx I am planning to spent at least 1 hour daily to learn Basic mathematics and Algebra I am trying to prepare for a test , that is why i wanted to learn all these from the beginning Now i need to find me some energy and motivation to sit and practice these books daily for at least 1 hour I am planning to study after 11 at night everyday , since i have to work till evening 6:30 everyday …

(61/2 - 21/2)/4 = (2 - 31/2)1/2/2 I have taken sin * cos=1/4 then I have got sine=(2 - 31/2)1/2/2 or (2 + 31/2)1/2/2 Calculator has shown arcsin=15 degrees but sine 15 degrees=(61/2 - 21/2)/4 I don't understand how they are connected.

Water Displacement Method This web-page says to use water displacement method to do so: https://sciencing.com/do-volume-object-6199021.html Another Way? But, is there a way to measure an irregular object without having to use the water displacement method for practical use with everyday objects? Gap Value The interesting thing about the formula for square or rectangled volume is that if used to measure irregular shaped objects, it would already contain gap information or gap values. The next step would be to find out how many amount gap number is then use total volume to subtract it to obtain an accurate volume for irregular object being …

To me, axiom-systems seem to basically be ownships (properties). For instance, the group-axiom-system is basically the ownship of being an ordered pair \((G, *)\) such that \(G\) is a set and \(*\) is a function from \(G\times G\) to \(G\) such that \(*\) is associative and has an identity element and each member of \(G\) has an inverse element with regard to \(*\). Just as the axiom-system itself is an ownship, so are what are called “propositions in the language/speech of the system” actually properties. For instance, when we say: “The proposition that the sum of the inner angles of a triangle is always 180° follows from the Euclidean axioms“, we actually mean tha…

I want to refresh some basic mathematics and i have difficulty getting some good notes on signed numbers Can anyone suggest me some good books to learn basic mathematics especially about signed numbers . Thanks

How do we solve polynomial equations? I only know how to simplify them. If you could solve this polynomial say N = 85 it would earn a million dollars. Remember who gave it to you. x^3 = N^2 * (x^2/(N^2/x + x)) Solve for x

Are there any good applications of research regarding spam/fake review detection?

I read that learning to use an abacus can help with one's own mental arithmetic... anyone experienced this? And any suggestions of a good abacus (type) to buy? Thanks in advance..

Do points lie on tangents lines "only?" From: "The slope of the tangent" Or on the curve itself?? If it's not on the curve, then: Where did that curve come from?? I'm not getting the ideas behind the following. ( x + delta h) I'm very familiar with linear equations but this does not clarify tangent points and the "fancy" albegra doesn't explain the evolution of time either cuz it sets everything at 0... Are these Points Hyper Planes?? Light Cones?? Faster Than Light Speeds?? N Gons?? Oragami?? ----->Standing Waves Maybe???

Is this as 2 pennies plus 6 pennies is 8 pennies?? could we also say 6/2 = 3 pennies Does this mean that all 3 pennies are1/2 * 6 pennies = smaller pennies? Im totally confused..

One thing I notice is that many shapes in 2-space; squares, circles, etc... can all have the common word "surface" apply to them. Even non-2-space descriptions like "the Earth's surface" still refer to the kinds of things that could intersect with each other at a point, along a line, along a curve, etc... just like 2-D shapes can. It seems the word surface more generally refers to that which is either 2-dimensional or could theoretically be unfurled to FORM something 2-dimensional. (Granted, if you did that with the Earth's surface a lot of people would get hypothermia pretty quickly!) Alternatively, it seems to refer to anything which Stokes' Theorem may apply to. Are th…

If x^2 = x/x = 1, why does 1 depend on 2 input values??? I get this idea from y' = 2x What if an input value was 3, does that make x cubed?????? y' =x^3 I'm totally confused..

Did Issac Newton know about numeral systems? IE Bases 10, 2, 1 etc etc? If not then, why do we use them "in calculus today??" Moreover, how can computers compute calculus? Issac Newton didn't have one, or did he?? Was it a Macintosh?? seriously.. This should be a very interesting thread..

As conciseness is one of main mathematical features, I would like to discuss one particular instance of it. Can someone please summarize in that context the usefulness of excluding number one from the set of prime numbers? As the definition of prime numbers would be more concise without it, ie if one was included, and in fact it was at the beginning, first great contributors to number theory who laid foundations to prime number theory considered it to be prime, exclusion was introduced later, without much change in the essence of the theory, so it must have payed off somehow in terms of development of shorter expressions of consequences of somewhat longer definition, and …

Is there a mathematical way to represent the formula itself? i.e. this sentence is about itself being informative

Whenever I write a sum in Latex, the limits appear forward of the sum sign. I have seen many instances where the limits are below and above. What is the code to get them there?