Trouble with Confusing Notations in Mathematics?

  • Context: Undergrad 
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Discussion Overview

The discussion revolves around the challenges posed by confusing and inconsistent mathematical notations, particularly in the context of functional notation. Participants explore the implications of these notations on learning and understanding mathematics, sharing personal experiences and suggestions for improvement.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant expresses frustration with the notation f(x) and its distinction from simple multiplication, suggesting that better notation could alleviate confusion.
  • Another participant argues that the notation is standard and that familiarity with it can be developed over time, emphasizing that f(x) represents a single entity rather than a multiplication operation.
  • Some participants propose that viewing functions as mappings between sets might provide clarity.
  • Concerns are raised about whether the aesthetic aspects of notation could deter students from engaging with mathematics.
  • There is a discussion about the variability of notation across different contexts, with some suggesting that a universal standard would be ideal, while others argue that context-specific notation is necessary.
  • One participant notes that different mathematical software uses distinct notations to avoid confusion, highlighting the inconsistency in notation across platforms.
  • Another participant mentions that the ambiguity of symbols could lead to philosophical considerations about the nature of mathematical truth and constructivism.
  • Some participants acknowledge that while notation can be cumbersome, consistency within a given context is crucial for understanding.

Areas of Agreement / Disagreement

Participants exhibit a mix of agreement and disagreement regarding the effectiveness and clarity of mathematical notation. While some believe that the current standards are adequate, others express concern about their potential to confuse learners. The discussion remains unresolved on whether a universal notation would be beneficial.

Contextual Notes

Participants note that the interpretation of symbols can vary significantly depending on the mathematical context, and there are unresolved questions about the implications of this variability for learning and understanding mathematics.

  • #31
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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