线性代数网课代修|ENGO361代写|ENGO361英文辅导|ENGO361

如果你也在线性代数linearalgebra这个学科遇到相关的难题,请随时添加vx号联系我们的代写客服。我们会为你提供专业的服务。 linearalgebra™长期致力于留学生网课服务,涵盖各个网络学科课程:金融学Finance,经济学Economics,数学Mathematics,会计Accounting,文学Literature,艺术Arts等等。除了网课全程托管外,linearalgebra™也可接受单独网课任务。无论遇到了什么网课困难,都能帮你完美解决! Thus we have a means of expressing universal and particular propositions when they are applied to variables, especially those in the form: “For every value of \(x\) such and such a proposition is true”, and “For some value of \(x\), such and such a proposition is true”, etc.For instance, the equivalence\[(a=b)=(ac=bc)(a+c=b+c)\]is somewhat paradoxical because the second member contains a term (\(c\)) which does not appear in the first. This equivalence is independent of \(c\), so that we can write it as follows, considering \(c\) as a variable \(x\)\[\prod_{x}[(a=b)=(ax=bx)(a+x=b+x)],\]or, the first member being independent of \(x\),\[(a=b)=\prod_{x}[(ax=bx)(a+x=b+x)].\]In general, when a proposition contains a variable term, great care is necessary to distinguish the case in which it is true for _every_ value of the variable, from the case in which it is true only for some value of the variable.37 This is the same as the case in which it is true only for some value of \(x\); that is to keep purpose that the symbols \(\prod\) and \(\sum\) serve.This is the same as the distinction made in mathematics between _identities_ and _equations_, except that an equation may not be verified by any value of the variable.Thus when we say for instance that the equation\[ax+bx^{\prime}=0\]is possible, we are stating that it can be verified by some value of \(x\); that is to say,\[\sum_{x}(ax+bx^{\prime}=0),\]and, since the necessary and sufficient condition for this is that the resultant \((ab=0)\) is true, we must write\[\sum_{x}(ax+bx=0)=(ab=0),\]although we have only the implication\[(ax+bx=0)

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