Curve where both x and y approach infinity

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Discussion Overview

The discussion revolves around identifying equations for curves where both x and y approach infinity. Participants explore various mathematical representations and properties of such curves, including straight lines and more complex functions.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant inquires about the equation for a curve where both x and y approach infinity.
  • Another participant suggests the equation ##x = y##, which leads to a discussion about whether this represents a curve or a straight line.
  • There is a clarification that a straight line is considered a type of curve, but an alternative suggestion is made with the equation ##x = y^2## for a more pronounced curvature.
  • One participant notes that there are many planar curves with the property that ##x \to \infty## as ##y \to \infty## and asks if any additional properties are being sought.
  • Another participant mentions that the equations ##y = \ln(x)## and ##y = e^x## also satisfy the condition of both variables approaching infinity.

Areas of Agreement / Disagreement

Participants express differing views on whether a straight line qualifies as a curve, and there is no consensus on a single equation that best represents the desired properties of the curve.

Contextual Notes

Participants have not specified any additional properties they are looking for in the curves, leaving the discussion open to interpretation and further exploration.

Pjpic
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What is the equation for a curve where x approaches infinity as y approaches infinity?
 
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I don't think I understand you well, but what about: ##x = y##
?
 
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Krylov said:
I don't think I understand you well, but what about: ##x = y##
?
Wouldn't that be a straight line instead of a curve?
 
Pjpic said:
Wouldn't that be a straight line instead of a curve?
To me a straight line is a particular kind of curve, but if you prefer something that really "curves", then you could do ##x = y^2##. However, I believe you were also able to find that out?

Maybe it helps when you explain a bit more about the background of your question. There are lots of planar curves with the property that ##x \to \infty## as ##y \to \infty##. Are you looking for a curve among them that has some additional properties?
 
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Krylov said:
To me a straight line is a particular kind of curve, but if you prefer something that really "curves", then you could do ##x = y^2##. However, I believe you were also able to find that out?

Maybe it helps when you explain a bit more about the background of your question. There are lots of planar curves with the property that ##x \to \infty## as ##y \to \infty##. Are you looking for a curve among them that has some additional properties?
I think I get it. Powers make a curve.
 
A straight line is a mathematical curve as well. It is just an interesting special case.
 
##y=ln(x)## also works as does ##y=e^x##
 

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