Pseudo Programmer

$R$ : ring with unity, $J$ : ideal of $R$. Suppose that unit $u \in J, \exists u\in R$. Then, $x \in R \implies x \cdot u^{-1} \in R \implies (x \cdot u^{-1}) \cdot u \in J \implies x \in J \  (\forall x \in R)$. Hence, $R \subseteq J$, and by definition of ideal, $J \subseteq R$. $\therefore R = J$

  'v.탄압하다, 억압하다'  라는 뜻으로 사용될 때, oppress는 힘이나 권력, 권한으로 누군가를 압박하고 탄압한다는 뜻이 강합니다. repress는 욕망, 감정 행동, 눈물등을 억누른다는 뉘앙스가 강하고, suppress는 앞의 두개에 비해서 더 넓은 의미로 사용됩니다. Example Sentences oppress Madison, in particular, worried that a majority might oppress minorities and that elected representatives might legislate out of "passion". [The Economist] They tout arguments about the existence of a monarchy being a root cause of oppression, economic decline, and no doubt soon global warming. [Telegraph] repress I have come to believe that seasoned reporters seem to somehow repress their natural instincts. [The Age] Anger, especially in men, is often an undiagnosed sign of depression and repressed grief that needs a healthy expression and healing. [National Review] suppress There is no evidence he has falsified or suppressed data. [Washington Post] Several candidates have complained their ridings are being targetted to annoy voters and possibly suppress the vote on electi

  'v.선언하다, 발표하다, 알리다' 라는 뜻으로 사용될 때, pronounce는 announce에 비해서 좀더 격식을 차려서 공식적(authoritative, explicit, formally)으로 말할 때 쓴다. 굳이 구분하지 않고 섞어서 쓰는 경우도 있는 것 같다. 하지만 아래 예문에서 볼 수 있듯이 중요한 일일 경우 pronounce를 쓰는 경우가 많다. Example Sentences announce The government yesterday announced to the media plans to create a million new jobs. We are pleased to announce that all five candidates were successful. It was announced that new speed restrictions would be introduced. pronounce I   now   pronounce   you   man   and   wife . He   pronounced   the   country   to   be   in   a   state   of   war . On the death of Mary queen of Scots he was chosen to  pronounce  her eulogy. Reference  [1] Oxford Advanced Learner's English-Korean Dictionary