What is an infinite sequence?

<正>Series will be introduced briefly in the following paper.It is important in calculus for Newton's idea of representing functions as sums of infinite series.In finding areas,he often integrated a function by expressing it as series.Now,we'll learn infinite sequences.     

What is an infinite series?

<正>Finite sequences and series have defined first and last terms,otherwise,infinite sequences and series continue indefinitely.Infinite series need tools from mathematical analysis,which are also widely used in other quantitative disciplines such as physics,computer science,and finance.Now we have an infinite sequence a_1,a_2,     

“What Counts as an Insult?”

In virtue of what does a linguistic act count as an insult? I discuss five main approaches to this question, according to which an insult is determined by (i) the semantic properties of the expression used; (ii) the insulter, her intention, or attitudes; (iii) the addressee and her personal standard; (iv) the features of the speech act performed; and (v) the standard of the relevant social group. I endorse the last, objectivist account, according to which an act x counts as an insult if and only if x is assessed as demeaning when addressed at A by the standard of the relevant social group at t.     

What portion of the sample makes a partial sum asymptotically stable or normal?

Summary Let a sequence of independent and identically distributed random variables with the common distribution function in the domain of attraction of a stable law of index 0<2 be given. We show that if at each stage n a number k _n depending on n of the lower and upper order statistics are removed from the n-th partial sum of the given random variables then under appropriate conditions on k _n the remaining sum can be normalized to converge in distribution to a standard normal random variable. A further analysis is given to show which ranges of the order statistics contribute to asymptotic stable law behaviour and which to normal behaviour. Our main tool is a new Brownian bridge approximation to the uniform empirical process in weighted supremum norms.Work done while visiting the Bolyai Institute, Szeged University, partially supported by a University of Delaware Research Foundation Grant     

What is the probability an automorphism fixes a group element?

Extending the notion of probability to the automorphisms of a group, we find the probability of an arbitrarily chosen automorphism of a group fixing an arbitrary element of the group.     

What lifts?

As is well known, idempotents in any ring R lift modulo any nil idea I. That is, if a ? R and (a₂-a) ? I there is an i ? I with (a + i)²-- (a + i) = 0. An idempotent is a zero of the polynomial x ²?x ², and a nil element satisfies x ⁿfor some n. Seen this way, lifting occurs in considerable generality We assume R has a unit, and handle the non-unital case at the end of this paper.     

Why is paper-and-pencil multiplication difficult for many people?

In school, at least in the US, we were taught to multiply by hand according to a standard algorithm. Most people find that algorithm difficult to use, and many children fail to learn it. We propose a new way to make sense of this difficulty: to treat explicit computation as perceptually supported physical and mental action. Based on recent work in neuroscience, we trace the flow of arithmetic information to emphasize demands on visual working memory and attention. We predict that algorithms that make moderate demands on memory and attention will work better than others that make stronger demands. We suggest that the judicious use of spatial schemas can reduce such cognitive demands. Experimental evidence from children in an inner-city school supports this claim. Our work suggests new ways to think about instruction. The goal should be to minimize demands that present obstacles and maximize instead what human eyes, bodies, and brains do well.     

What is continuity?

A continuous process is a person who draws the curve without a break,or,takes place gradually without interruption. Those are a daily language in continuity. However,in calculus,we notice that the limit of a function as x approaches a can often be found simply by calculating the value of the function at a. It means a continuous function     

What Is Entitlement?

In his seminal paper, “Content Preservation,” Tyler Burge defends an original account of testimonial knowledge. The originality of the account is due, in part, to the fact that it is cast within a novel epistemic framework. The central feature of that framework is the introduction of the concept of entitlement, which is alleged to be a distinctive type of positive epistemic support or warrant. Entitlement and justification, according to Burge, are sub-species of warrant. Justification is the internalist form of warrant, but entitlement is epistemically externalist. My focus in this paper is Burge’s conception of entitlement, and there are three primary issues that I wish to address. What is the relationship between entitlement and the more traditional concept of justification? In what sense is entitlement epistemically externalist? Has Burge introduced a new epistemic concept or merely coined a new term for a familiar epistemic concept?     

What part of the concept of acceleration is difficult to understand: the mathematics, the physics, or both?

In this paper, details of student difficulties in understanding the concept of acceleration and the mathematical and physical/intuitive sources of these are delineated by utilizing the teaching experiment methodology. As a result of the study, two anchoring analogies are proposed that can be used as a diagnostic tool for students’ alternative conceptions. These can be used in teaching to highlight the peculiarity of acceleration concept. This study portrays how seeing acceleration as ‘rate of change’ of a quantity (velocity) and recognizing the consequences of such a definition are hindered in certain ways which in turn negatively affect learning the concept of force. This is also an example that illustrates that a rather “simple” mathematical concept (i.e., rate of change) for the expert can become a complex phenomenon when embedded in a physical concept (i.e., acceleration) which is consistently found to be as a misconception among learners at various levels that is widely occurring and very resistant to change.     

What Norm of Assertion?

I argue that the debates over which norm constitutes assertion can be abandoned by challenging the three main motivations for a constitutive norm. The first motivation is the alleged analogy between language and games. The second motivation is the intuition that some assertions are worthy of criticism. The third is the discursive responsibilities incurred by asserting. I demonstrate that none of these offer good reasons to believe in a constitutive norm of assertion, as such a norm is understood in the literature. Others who have made similar arguments conclude that assertion does not exist at all—that there is no such thing as assertion. I disagree: we do not have to relinquish the category of assertion just because it is not normatively constituted. There are alternative ways to understand and individuate assertion that do not rely on a constitutive norm.