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supposition

supposition (sʌpəˈzɪʃən) [ad. L. suppositio, -ōnem, n. of action f. supposit-, suppōnĕre to suppone. Cf. F. supposition, It. supposizione, Sp. suposicion, Pg. supposi{cced}ão. The current meanings arose from the equation of med.L. suppositio to Gr. ὑπόθεσις hypothesis, of which it is the etymologica... Oxford English Dictionary

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Supposition theory

He proposed calling the subvarieties of personal supposition a theory of "modes of supposition." This kind of personal supposition is called discrete supposition. wikipedia.org

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supposition

supposition/ˌsʌpəˈzɪʃn; ˌsʌpə`zɪʃən/ n1 [U] supposing 假定; 猜想; 推测 a newspaper article based on supposition, ie only on what the writer supposes to be true, not on fact 根据臆想写出的报刊文章 We must not condemn her on pure supposition. 我们不能单凭臆测而谴责她.2 [C] ~ (that...) thing supposed; guess 假定的事物; 猜测 Our supposit... 牛津英汉双解词典

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General conditional (-えば form) expressing something without supposition or back thought? I found a resource which says the _-eba_ form is a form used to express a conditional without supposition or back thought. I d...

I read the explanation given in the link and it may be confusing to state it like this. In fact, the ~conditional form suppose no constraint on the context and is the most "open" conditional form. It implies that the condition (sentence in ) is less probable to happen compared to the other condition...

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Suppose there always exist pairs of finite automata that recognize L and the complement of L, respectively. What does this imply? Suppose there always exist pairs of finite automata that recognize L and the complement...

**Hint**. Regular languages are closed under complementation. EDIT. A language is regular if and only if it is recognized by a finite automaton. Now, knowing that there exist pairs of finite automata that recognize a language and its complement, respectively, just means that the language is regular....

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Equality of two complex numbers with respect to argument If two complex numbers are equal , is it necessary that their arguments are also equal ? Is the vice versa also true ? means that if the arguments of two comple...

If we take complex numbers as $z_1 = a+bi$ and $z_2 = c+di$, $z_1 = z_2$ if and only if $a = c$ and $b = d$. So $\arg(z_1) = \arg(z_2)$, obviously. However, if $\arg(z_1) = \arg(z_2)$, it doesn't have to imply that $z_1 = z_2$. A simple counter-example is $z_1 = 2z_2$ with $z_1 \ne 0$. Their argumen...

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supposition Approprié collier chaussons aux crevettes nouvelles ...

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Bounded Mean of Partial Sums and Convergence This is from Amemiya's Advanced Econometrics Chapter 3 Q5: Suppose $\\{a_t\\}$ is a non-negative sequence such that $\frac{1}{T}\sum_{t=1}^{T} a_t < M$ for all $T$. Prove ...

Let $A_T = \sum_{t=1}^T a_t$. Summation by parts yields $$ \sum_{t=1}^T \frac{a_t}{t^2} = \frac{A_T}{(T+1)^2} + \sum_{t=1}^TA_t\left( \frac{1}{t^2} - \frac{1}{(t+1)^2}\right) \\\ = \frac{A_T}{T}\frac{T}{(T+1)^2} + \sum_{t=1}^T\frac{A_t}{t}\left( \frac{2t+1}{t(t+1)^2} \right). $$ The first term on th...

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Prove that $f$ is an increasing function if $f'(x)$ is more than zero for all real values for $x$ I'm having some difficulty with proving this theory. What I do know is how to prove that it is a constant function when...

$f'(x) > 0$ everywhere means $f$ is continuous everywhere. And the mean value theorem says that for any $a, b; a 0$ so $f(b) > f(a)$.

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Is this contradiction proof correct? Statement : suppose $a,b$ belongs to $\mathbb{Z}$ (integers). If $4/ (a^2 + b^2)$ then $a$ and $b$ are not both odd. Proof by contradiction: Assume that if $4/(a^2 + b^2)$ then a ...

The proof by contradiction should start with > assume that $a$ and $b$ are both odd and $4\mid (a^2+b^2)$ You can continue by saying > write $a=2h+1$ and $b=2k+1$ and > so that $a^2+b^2=4h^2+4h+1+4k^2+4k+1=\dots$ Now you can add > and we have a contradiction, because this would imply $\dots$

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のなら: emphasis or hearsay? What is the additional nuance in meaning when is inserted before ? For example: > () In the Tobira Gateway to Advanced Japanese (p. 69) it says > occurs before when the supposition is b...

This is an explanatory-. Roughly speaking, it adds the nuance of "(if) ... is the case" or "(if) it's that ...". This is usually optional, but it indicates the conditional is something that does matter now. You can use to seek clarification in an interrogative sentence (see this). This connotation i...

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Let $f : (a,b)\to\mathbb{R}$ be continuous and diﬀerentiable on $(a,b)$ and diﬀerentiable at a point k. Does $\lim_{x\to k} f'(x)$ exist? I'd like to prove that this proposition holds. Is it enough to say that by supp...

If f is not differentiable, no... If $f$ is not differentiable at $k$, then no. For instance, take $x\mapsto|x|$. Its derivative coincides with$\frac{|x|}{x}$ for every $x\in(a,b)\setminus \\{0\\}$, but is not defined in $0$. You can easily see that $$ \lim_{x\to 0^{+}}\frac{|x+h|-|x|}{h}=\frac{x+h-...

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If $A$ and $B$ are bounded sets show that $A⊂B$ implies $\mathrm{diam}(A)≤ \mathrm{diam}(B)$ Below is what I attempt, Let $\mathrm{diam}(A) < m$ and $\mathrm{diam}(B) < n$ Let $A⊂B$ Say, $\mathrm{diam}(A)> \mathrm{...

$\newcommand{\diam}{\text{diam}}$ $$\diam(A)=\sup\\{\|x-y\|\mid x,y\in A\\}\quad\text{and}\quad \diam(B)=\sup\\{\|x-y\|\mid x,y\in B\\}.$$ Since $A\subset B$,$$\\{\|x-y\|\mid x,y\in A\subset B\\}\subset \\{\|x-y\|\mid x,y\in B\\}.$$ The result follows. The thing you can add is the proof of $$A\subse...

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Automorphisms of order 2 Let $G$ be a finite group with no element of order $p^2$ for each prime $p$. Does there always exist an automorphism $\phi$ of order 2 such that for at least one subgroup of $G$ say $H$, we ha...

A quick counter-example is any cyclic group $C_p$ of prime order $p>2$. There's no element of order $p^2$ and for any automorphism $\phi$, we have $\phi(\\{1\\})=\\{1\\}$ and $\phi(C_p)=C_p$ so there is certainly no automorphism of order $2$ with subgroup $H$ of $G$ with $\phi(H)\ne H$

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Orientable manifold with finite first homology group. I've started going through old comps and have hit a road block, the following: Let $M$ be a closed, connected, orientable $n$-manifold, with $n \geq 3$. Show if $...

If $H_{1}(M)$ is finite then by the universal coefficient theorem, $$H^1(M) \cong \hom_{\mathbb{Z}}(H_1(M), \mathbb{Z})$$ is zero (because $\mathbb{Z}$ has no nonzero elements of finite order). And by Poincaré duality (the manifold is connected, closed, and orientable), there is an isomorphism $H_{n...

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supposition

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supposition

Supposition theory

supposition

General conditional (-えば form) expressing something without supposition or back thought? I found a resource which says the _-eba_ form is a form used to express a conditional without supposition or back thought. I d...

Suppose there always exist pairs of finite automata that recognize L and the complement of L, respectively. What does this imply? Suppose there always exist pairs of finite automata that recognize L and the complement...

Equality of two complex numbers with respect to argument If two complex numbers are equal , is it necessary that their arguments are also equal ? Is the vice versa also true ? means that if the arguments of two comple...

supposition Approprié collier chaussons aux crevettes nouvelles ...

Bounded Mean of Partial Sums and Convergence This is from Amemiya's Advanced Econometrics Chapter 3 Q5: Suppose $\\{a_t\\}$ is a non-negative sequence such that $\frac{1}{T}\sum_{t=1}^{T} a_t < M$ for all $T$. Prove ...

Prove that $f$ is an increasing function if $f'(x)$ is more than zero for all real values for $x$ I'm having some difficulty with proving this theory. What I do know is how to prove that it is a constant function when...

Is this contradiction proof correct? Statement : suppose $a,b$ belongs to $\mathbb{Z}$ (integers). If $4/ (a^2 + b^2)$ then $a$ and $b$ are not both odd. Proof by contradiction: Assume that if $4/(a^2 + b^2)$ then a ...

のなら: emphasis or hearsay? What is the additional nuance in meaning when is inserted before ? For example: > () In the Tobira Gateway to Advanced Japanese (p. 69) it says > occurs before when the supposition is b...

Let $f : (a,b)\to\mathbb{R}$ be continuous and diﬀerentiable on $(a,b)$ and diﬀerentiable at a point k. Does $\lim_{x\to k} f'(x)$ exist? I'd like to prove that this proposition holds. Is it enough to say that by supp...

If $A$ and $B$ are bounded sets show that $A⊂B$ implies $\mathrm{diam}(A)≤ \mathrm{diam}(B)$ Below is what I attempt, Let $\mathrm{diam}(A) < m$ and $\mathrm{diam}(B) < n$ Let $A⊂B$ Say, $\mathrm{diam}(A)> \mathrm{...

Automorphisms of order 2 Let $G$ be a finite group with no element of order $p^2$ for each prime $p$. Does there always exist an automorphism $\phi$ of order 2 such that for at least one subgroup of $G$ say $H$, we ha...

Orientable manifold with finite first homology group. I've started going through old comps and have hit a road block, the following: Let $M$ be a closed, connected, orientable $n$-manifold, with $n \geq 3$. Show if $...