4 ms·

It depends, I think. In some circumstances ∞ is just a special number, as 0 is a special number. Consider the operation (||) of parallel coupling of resistors

by jonsen 17y ago

It depends, I think. In some circumstances ∞ is just a special number, as 0 is a special number. Consider the operation (||) of parallel coupling of resistors 1Ω || 1Ω = 1/2Ω cf. 1Ω + 1Ω = 2Ω 1Ω || 0Ω = 0Ω cf. 1Ω + 0Ω = 1Ω 1Ω || ∞Ω = 1Ω cf. 1Ω + ∞Ω = ∞Ω For the operator || ∞ is the identity element as 0 is for operator +

tokenadult 17y ago
Do we really consider infinite resistance a numerical value of (a measurement of) resistance?
- jonsen 17y ago
  No we don't consider ∞ a numerical value. The big question is: Is it a value nonetheless? Edit: Infinite resistance is as well defined as zero resistance. Infinite resistance equals zero conductance. Infinite conductance equals zero resistance. Edit2: So if you measure the conductance of an infinite resistor you get the numerical value 0.
  - tokenadult 17y ago
    I think this reasoning ends up being something like dividing by zero. A measurement of "infinity" can't be in any definable place on interval scale.
    - jonsen 17y ago
      Well then a measurement of zero can't be in any definable place on interval scale either.
      - tokenadult 17y ago
        Above you wrote, No we don't consider ∞ a numerical value. So you are agreeing with the title and with the substance of the submitted article, which I submitted for truth and for admiration of how it was written. As for an interval scale http://en.wikipedia.org/wiki/Level_of_measurement#Interval_scale http://en.wikipedia.org/wiki/Level_of_measurement#Interval_s... the zero point is well defined as the midpoint between -1 and 1, that is halfway between the values defined by those numbers. (It is commonly noted that the numerical designation of any point on such a scale is arbitrary, and the familiar examples are the Fahrenheit and Celsius scales of temperature, each with a different zero point, which in both cases is equidistant between -1 and 1.) No comparable definiteness of position is enjoyed by "infinity." Psychologist Joel Michell makes the very good point that his fellow psychologists are probably abusing language by referring to interval scales as "measurements," http://www.questia.com/library/book/an-introduction-to-the-logic-of-psychological-measurement-by-joel-michell.jsp http://www.questia.com/library/book/an-introduction-to-the-l... but for our purposes here it is enough to note that you, I, and the whole world notice that zero has a place on an interval scale if such a place is arbitrarily set, but infinity does not have such a place.
        jonsen 17y ago
        I think infinity is well enough defined - for measurements at least - on the reciprocal scale: -4 -3 -2 -1 0 1 2 3 4 --|----|----|----|----|----|----|----|----|-- -1/4 -1/3 -1/2 -1 ∞ 1 1/2 1/3 1/4 --|----|----|----|----|----|----|----|----|-- I certainly didn't intend to devaluate the submitted article. Just wanted to point at some circumstances where infinity in fact is considered a distinct and definable value; by the example of resistance being the reciprocal of conductance.
        tokenadult 17y ago
        That's still a division by zero error. Division by zero is no more valid in engineering than it is in mathematics. While I was out on a walk in my neighborhood I thought about the practical engineering problem you first mentioned above: whatever kind of resistor you are talking about, I think a lot less than infinite electricity could jump the gap filled by any finitely sized resistor, even if you initially regard it as having infinite resistance for purposes of analyzing the circuit. But I will leave further discussion of this point to readers here who have formal training and experience with electrical engineering, as my childhood best friend does. I'm not aware that he considers infinity a number or that he puts it anywhere on the number line. http://mathforum.org/dr.math/faq/faq.divideby0.html http://mathforum.org/dr.math/faq/faq.divideby0.html http://mathworld.wolfram.com/DivisionbyZero.html http://mathworld.wolfram.com/DivisionbyZero.html http://en.wikipedia.org/wiki/Division_by_zero http://en.wikipedia.org/wiki/Division_by_zero

by jonsen 17y ago

tokenadult 17y ago

Do we really consider infinite resistance a numerical value of (a measurement of) resistance?

jonsen 17y ago
No we don't consider ∞ a numerical value. The big question is: Is it a value nonetheless? Edit: Infinite resistance is as well defined as zero resistance. Infinite resistance equals zero conductance. Infinite conductance equals zero resistance. Edit2: So if you measure the conductance of an infinite resistor you get the numerical value 0.
- tokenadult 17y ago
  I think this reasoning ends up being something like dividing by zero. A measurement of "infinity" can't be in any definable place on interval scale.
  - jonsen 17y ago
    Well then a measurement of zero can't be in any definable place on interval scale either.
    - tokenadult 17y ago
      Above you wrote, No we don't consider ∞ a numerical value. So you are agreeing with the title and with the substance of the submitted article, which I submitted for truth and for admiration of how it was written. As for an interval scale http://en.wikipedia.org/wiki/Level_of_measurement#Interval_scale http://en.wikipedia.org/wiki/Level_of_measurement#Interval_s... the zero point is well defined as the midpoint between -1 and 1, that is halfway between the values defined by those numbers. (It is commonly noted that the numerical designation of any point on such a scale is arbitrary, and the familiar examples are the Fahrenheit and Celsius scales of temperature, each with a different zero point, which in both cases is equidistant between -1 and 1.) No comparable definiteness of position is enjoyed by "infinity." Psychologist Joel Michell makes the very good point that his fellow psychologists are probably abusing language by referring to interval scales as "measurements," http://www.questia.com/library/book/an-introduction-to-the-logic-of-psychological-measurement-by-joel-michell.jsp http://www.questia.com/library/book/an-introduction-to-the-l... but for our purposes here it is enough to note that you, I, and the whole world notice that zero has a place on an interval scale if such a place is arbitrarily set, but infinity does not have such a place.
      - jonsen 17y ago
        I think infinity is well enough defined - for measurements at least - on the reciprocal scale: -4 -3 -2 -1 0 1 2 3 4 --|----|----|----|----|----|----|----|----|-- -1/4 -1/3 -1/2 -1 ∞ 1 1/2 1/3 1/4 --|----|----|----|----|----|----|----|----|-- I certainly didn't intend to devaluate the submitted article. Just wanted to point at some circumstances where infinity in fact is considered a distinct and definable value; by the example of resistance being the reciprocal of conductance.
        tokenadult 17y ago
        That's still a division by zero error. Division by zero is no more valid in engineering than it is in mathematics. While I was out on a walk in my neighborhood I thought about the practical engineering problem you first mentioned above: whatever kind of resistor you are talking about, I think a lot less than infinite electricity could jump the gap filled by any finitely sized resistor, even if you initially regard it as having infinite resistance for purposes of analyzing the circuit. But I will leave further discussion of this point to readers here who have formal training and experience with electrical engineering, as my childhood best friend does. I'm not aware that he considers infinity a number or that he puts it anywhere on the number line. http://mathforum.org/dr.math/faq/faq.divideby0.html http://mathforum.org/dr.math/faq/faq.divideby0.html http://mathworld.wolfram.com/DivisionbyZero.html http://mathworld.wolfram.com/DivisionbyZero.html http://en.wikipedia.org/wiki/Division_by_zero http://en.wikipedia.org/wiki/Division_by_zero