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Nov 18, 2014 · This is a singleton, so $x\ne\emptyset=\bigcup x$. You are probably more used to seeing $\cup$ as a binary relation, written in between two sets, while $\bigcup$ is unary, written preceding the set it acts on. Perhaps that's the source of the confusion. The notation is quite precise here, there is no ambiguity. $\endgroup$ –
Usually, the conversion to another notation requires to scale the argument or the resulting value; sometimes, the same name of the function is used, causing confusions. Examples of such underestablished functions: Sinc function
The phrase "if no confusion" is grammatically correct and can be used in written English. It is typically used in conditional or hypothetical statements to clarify that something will only happen if there is no confusion or misunderstandings present.
When no confusion is possible, notation f(S) is commonly used. 1. Closed interval : if a and b are real numbers such that a ≤ b {\displaystyle a\leq b} , then [ a , b ] {\displaystyle [a,b]} denotes the closed interval defined by them.
Apr 19, 2023 · The original notation, using the square root symbol for imaginary numbers, led to misunderstanding and confusion in mathematics. For example, people might think that √− 1 ⋅ √− 1 = √− 1 ⋅ − 1 = √1, which is clearly incorrect when working with imaginary numbers.
Jun 4, 2016 · In statistics or machine learning literate (from book Elements of Statistical Learning) people use different notation to represent the same thing: $$X \beta= y$$ Where $X$ is the data matrix , $\beta$ is the coefficients or weights to be learned learning , $y$ is the response.
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Which notation is used when no confusion is possible?
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What font do you use for a quantifier expression?
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Is abuse of notation a reason?
As a rule of thumb I use type-writer font for quantifier expressions and italics for the signified quantifiers. In logical languages, on the other hand, it is convenient to abuse notation somewhat by using the same symbol for both the expression and the quantifier, when no confusion results.
