Development Process – Can someone give a clear definition of iterative SDLC and incremental SDLC?

Can someone give a clear definition of iterative SDLC and incremental SDLC?
And as part 3, the differences between the two.
I've seen a question posted here years ago and the question was closed even though 97,000 people wanted to see the answer. There was an attempt to answer that question which was not clear to me.

Note 1: Previous similar question in 2014.
Difference between incremental and iterative approach (closed)

Reference 2:
Alistair Cockburn (Crystal Software Process Model Creator) pointed out that the concepts are difficult to explain. Here is a quote from his article (2008) at: http://alistair.cockburn.us/Incremental+means+adding%2c+iterative+means+reworking Here's the relevant quote: "This is my 5th or 8th. Try to Describe the difference between incremental and iterative development, because with luck, reading will be more fun and easier to understand.

Field theory – What is the definition of a scalar?

In physics, a scalar is usually defined as a quantity that is completely defined by a size and no direction. This is not a good definition, as a complex number under this definition is not a scalar.

A second definition of a scalar is a variable that transforms as a scalar (for example, unchanged) when the coordinates are changed. This allows for pseudo-scalars and is useful for teaching physics students vectors and tensors. However, I suspect that a mathematician contradicts this definition because it relies on coordinates.

A third definition is that "a scalar is an element of a field used to define a vector space." However, this has no content, unless I am told what constitutes something allowed Element of a field. Does it have to have certain characteristics like a commutative, closed, binary operation with an identity? Does the concept of a scalar exist independently of the concept of a field?

Abstract Algebra – Why is the definition of Koprime / Comaximal ideals $ I + J = R $?

Two questions

To let $ R $ be commutative and have $ 1_R $, Two ideals are called caprime / comaxmal if $ I + J = R $

(1) The above is synonymous with the statement that it exists $ i + j = 1_R $, But for me this condition should be a definition and everywhere (ie Chinese memory) the element condition is used, never $ I + J = R $, So why do not we just say Coprime / Comaximal if $ i + j = 1_R $?

(1) I understand why it's called co-prime, but what does co-maximum mean? Co means together, and what has to do with it? We have no PID.

Functional Programming – What is the relationship between the formal definition of rigor and its intuitive concept?

The intuition: when it is executed f(x) causes x be evaluated and evaluated x does not end, then this will cause f(x) do not finish (because evaluate x will not finish the execution of f(x) never completes).

So, when it's done f(x) always caused x then be executed f will be strict by the above formal definition. Therefore "f(x) fully evaluated x"implies"f(x) evaluates down for everyone x evaluate downwards ".

In contrast, it is evaluated with a lazy function f(x) does not necessarily trigger the evaluation of xso that it does not necessarily end (even if it is evaluated) x would not cancel). In an intuitively lazy function, therefore, the formal definition of strict is not met.

real analysis – clarification of the definition of the lim sup of a set.

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ct.category theory – Definition of local epimorphism by homotopy colimit of the nerve Cech

To let $ f: A to B $ be a map between Presheaves of Mengen. That's what you say $ f $ is a local epimorphism if a card is given $ mathbf {y} X to B $There is a lid strainer $ R hookrightarrow mathbf {y} X $ so for every element $ U_i to X $ in the $ R $There is an elevator $ mathbf {y} U_i to A $ (from where y denotes the Yoneda embedding).

To let $ C (f) $ be the Cech-nerve of $ f $, How to show that the definition for $ f $ Being a local epimorphism is tantamount to saying that $ operatorname {hocolim} C (f) to B $ is a deck screen?

dg.differential geometry – Suggested problems for undergraduate students, inspired by the definition of Schwarz's derivative

In the past, I knew the so-called Schwarz derivative from an article in the AMS Notices ((1)). If I remember correctly, I have never encountered this definition. I was wondering what could be a good exercise or a problem for students with a bachelor's degree in relation to this definition ((1) illustrates some examples). Since I am not a professor, I am unable to get another proposal with a good mathematical content, but I note that it may be possible: Perhaps a question related to this derivation may be related to existence and the unity of ordinary solutions yields differential equations, … or in the context of numerical analysis methods for differential analysis or questions from the complex analysis or geometry that are affordable for undergraduate students (the undergraduate students can use their knowledge to solve them).

Question. Imagine you need to create an exercise / problem for an Assigment or Exam of a maths degree for students and want to present it with the Schwarz's Derivative. What is your original and real problem that you can introduce to the students? Explain if you want to determine the mathematical content of your proposal and solution. Many thanks.

So I hope this question is welcome as a small collection of real / original problems for students related to the Schwarz derivative, this Wikipedia, after some suggestions I should accept an answer.

I add the hint that comes from the famous and interesting section WHAT IS… the notices of the AMS

references:

(1) Valentin Ovsienko and Sergei Tabachnikov, WHAT IS … the Blackian
Derivative?
, Communications of the AMS, Volume 56, Number 1 (January 2009).