Trouble with Confusing Notations in Mathematics?

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Confusion surrounding mathematical notation, particularly functional notation, is a common issue among students, especially in fields like economics. Many find that the notation, such as f(x) not equating to f = 5, creates mental obstacles that hinder understanding. While some argue for more standardized notation, others emphasize the importance of context in interpreting symbols correctly. The discussion highlights the aesthetic discomfort with certain notations and the need for students to adapt to varying meanings across different mathematical contexts. Overall, the conversation reflects a broader concern about how notation may affect students' engagement with mathematics.
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Like Masta Coda said, trying to get everyone to use the same notation is like trying to get everyone to use the same language. Plus some notations are better than others for only certain situations. I had the same problem as you with f(x) not being f multiplied by x. f and x are never constantly a function and a variable of a real number. What I find is best is to never consider a(b) as a being multiplied by b but always when only the second variable is in parenthesis to understand the first as a function of the second. Represent multiplication with both parenthesis, a dot, or no parenthesis in the case of variables.
(f)(x)=fx=f*x= 5x
f=5
Part of notation is the ease of writing and communicating it. I still find it confusing how ordered pairs and interval notation can look exactly alike with parenthesis. (a,b) could mean the point or the interval. The keyboards inability to neatly express many things in math also annoys me.
 

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