An opinion is a person's ideas and thoughts towards something. It is an assessment, judgment or evaluation of something. An opinion is not a fact, because opinions are either not falsifiable, or the opinion has not been proven or verified.
In economics, philosophy, or other social sciences, analysis based on opinions is referred to as normative analysis (what ought to be), as opposed to positive analysis, which is based on scientific observation (what materially is). In mathematics and logic there can be no opinions about some claims, equations, and arguments, because often these kinds of statements are either valid or invalid, and true or false, and not open to contradicting opinions.
Historically, the distinction of proven knowledge and opinion was articulated by some Ancient Greek philosophers. Plato's divided line is a useful distinction between knowledge and opinions that is explained through the character of Socrates
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