What is the maximum of x and y?

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Discussion Overview

The discussion revolves around the concept of "maximum" as it applies to a set of numbers, specifically in the context of variables x and y. Participants explore the meaning of maximum in relation to independent variables, local maxima in graphical representations, and stationary points in calculus.

Discussion Character

  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant questions the meaning of "maximum" when referring to the set {x, y} and seeks clarification.
  • Another participant asks whether x and y are independent variables, implying a potential relationship between them.
  • A different participant suggests plotting specific coordinates and inquires about the local maximum around x=0, indicating a focus on graphical interpretation.
  • There is a question about whether {x, y} represents coordinates on a curve or the actual point of a relative maximum.
  • One participant introduces the concept of stationary points, stating that for a maximum, the gradient of the tangent must equal 0, and provides examples of functions with minimum and maximum stationary points.
  • Another participant reiterates their confusion regarding the maximum of {x, y} and provides a conditional definition based on the values of x and y.

Areas of Agreement / Disagreement

Participants express varying levels of understanding regarding the concept of maximum, with some seeking clarification while others provide definitions and examples. There is no consensus on the interpretation of maximum in this context, and multiple viewpoints remain present.

Contextual Notes

Participants do not fully agree on the definitions or implications of maximum, and there are unresolved questions about the relationship between x and y, as well as the nature of the points being discussed.

ghostchaox
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What is the "maximum"

I don't understand what this is supposed to mean when used with a set of numbers like:

maximum of {x,y}

Can anybody help?
 
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Are x and y independent variables?
 
Plot these numbers as a smooth line:

-1,-1
0,0
1,-1

What is the local maximum around x=0?
 
Is {x,y} a set of coordinates on the curve? Or are they the actual point of the relative maximum.
 
Well if you mean extremas, then you {x,y} must be a stationary point where the gradient of the tangent is equal to 0.

If so, then it is talking about the nature of the curve. An example is:
consider the graphs of the following...
y=x^2, at x=0, it is a minimum stationary point.
y=-x^2, at x=0, it is a maximum stationary point.
 
ghostchaox said:
I don't understand what this is supposed to mean when used with a set of numbers like:

maximum of {x,y}

Can anybody help?

Based on what you wrote,

maximum of {x,y} =
x, if x>=y
y, otherwise
 

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