Glossary entry (derived from question below)
Spanish term or phrase:
aumenta hasta llegar a una asíntota para n=∞
English translation:
increases until reaching an asymptote for n = (infinite symbol)
Added to glossary by
Nicholas Callaway
May 19, 2011 13:03
13 yrs ago
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Spanish term
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aumenta hasta llegar a una asíntota para n=∞
Spanish to English
Science
Nuclear Eng/Sci
neutron activation analysis
"Al incrementar n, AT*n cycles(a) aumenta hasta llegar a una asíntota para n= ∞."
How can I phrase the last part of the sentence, "hasta llegar a una asíntota para n= ∞"?
The paper is on neutron activation analysis. Here n is the number of cycles, the function is some value or other that needs to be maximized (math is not my strong point), and these two factors from the irradiation trials are being analyzed with an algorithm.
How can I phrase the last part of the sentence, "hasta llegar a una asíntota para n= ∞"?
The paper is on neutron activation analysis. Here n is the number of cycles, the function is some value or other that needs to be maximized (math is not my strong point), and these two factors from the irradiation trials are being analyzed with an algorithm.
Proposed translations
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Proposed translations
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Julio Carmiol
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Related KudoZ points
:
4
Selected
increases until reaching an asymptote for n = (infinite symbol)
I am an engineer and we used to see this concept in a branch of Math called Limits
An asymptote is a line towards which a curve for a formula (as seen on a graph) tends to closer and closer without ever arriving. If you were developing a 100% reliable process, and first you got 90% success, then 98% success, then 99.9% success, then 99.999% success, and it kept on increasing, but you could expect this to never arrive fully at
100%, then this behavior would be an asymptotic curve, the asymptote being 100%
A formula that would follow sucha behavior would be f(n)=1/n.
If you graph the results, in a 2 dimensional graph, with n on the horizontal line, and f(n) on the vertical line, you would get:
n. f(n)
1. , 1
2. , 0.5
3. , 0.333
100, 0.01
1000, 0.001
As n increases, tending towards infinite, the result would get closer and closer to cero, but will never quite be zero, so the asymptote in this case would be a horizontal line, drawn at 0, or what is usually called in math the x axis.
.
Here is what the Merriam Webster dictionary says about that word.
Definition of ASYMPTOTE
: a straight line associated with a curve such that as a point moves along an infinite branch of the curve the distance from the point to the line approaches zero and the slope of the curve at the point approaches the slope of the line
— as·ymp·tot·ic adjective
— as·ymp·tot·i·cal·ly adverb
Illustration of ASYMPTOTE
--------------------------------------------------
Note added at 2 hrs (2011-05-19 15:45:45 GMT)
--------------------------------------------------
The term asymptote defines what is happening, which is this asymptotic behavior.
An asymptote is a line towards which a curve for a formula (as seen on a graph) tends to closer and closer without ever arriving. If you were developing a 100% reliable process, and first you got 90% success, then 98% success, then 99.9% success, then 99.999% success, and it kept on increasing, but you could expect this to never arrive fully at
100%, then this behavior would be an asymptotic curve, the asymptote being 100%
A formula that would follow sucha behavior would be f(n)=1/n.
If you graph the results, in a 2 dimensional graph, with n on the horizontal line, and f(n) on the vertical line, you would get:
n. f(n)
1. , 1
2. , 0.5
3. , 0.333
100, 0.01
1000, 0.001
As n increases, tending towards infinite, the result would get closer and closer to cero, but will never quite be zero, so the asymptote in this case would be a horizontal line, drawn at 0, or what is usually called in math the x axis.
.
Here is what the Merriam Webster dictionary says about that word.
Definition of ASYMPTOTE
: a straight line associated with a curve such that as a point moves along an infinite branch of the curve the distance from the point to the line approaches zero and the slope of the curve at the point approaches the slope of the line
— as·ymp·tot·ic adjective
— as·ymp·tot·i·cal·ly adverb
Illustration of ASYMPTOTE
--------------------------------------------------
Note added at 2 hrs (2011-05-19 15:45:45 GMT)
--------------------------------------------------
The term asymptote defines what is happening, which is this asymptotic behavior.
4 KudoZ points awarded for this answer.
Comment: "All of your answers were very helpful. I think that if I had to write the paper I would opt for DLyons's response, but as it's not my job to correct their mathematical terminology and make it more precise, I feel more comfortable using Julio's more direct translation. Thank you all for your detailed explanations!"
+2
3 mins
increases to an asymptote for n = ∞
increases to an asymptote for n = ∞
Peer comment(s):
| agree |
Antoni Morey i Pasqual
14 mins
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thank you
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| agree |
Peter Clews
: Not necessarily the best way to say it, but your answer is correct and you got there first.
5 hrs
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thank you
|
23 mins
The function tends to a (finite) limit as n tends to infinity.
From your description, I'm not entirely sure what "The function" is.
Can you post it?
Can you post it?
Peer comment(s):
| neutral |
Neil Ashby
: "tends" to infinity is not the equals symbol! I believe it is > or =>. And besides how can you give a confidence of 5 if your are not sure what the function is???
33 mins
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Since the number of cycles is finite, n=infinity can only be a fairly mathematically imprecise shorthand for "tends to infinity". And I was only offering a more precise translation by including the function in a note. Trust me :-)
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| neutral |
Peter Clews
: "tends to infinity" is correct. The expression "n = ∞" can't mean literally "n equals infinity", since this means that n+1 would be greater than infinity, meaning that infinity is not infinite
4 hrs
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Thanks pclews. You're absolutely right that this can't mean literally "n equals infinity",
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Discussion
"On incrementing n, AT*n cycles(a) increases, reaching an asymptote when n= ∞." n is the number of cycles (of the irradiation trial, its values are n=1, 2, 3, ...) but it's not clear what AT*n cycles(a) is - some sort of function of n, call it f(n) to use standard notation.
The above may be the best way to translate the sentence, but it's mathematically sloppy and should be written as something like
"f(n) is a monotonically increasing function of n which tends towards (value of asymptote) as n=1, 2, 3, ... tends to infinity."
"n = ∞" should really not be written in this context.
you'll see the curve asyptotically approaching a straight line as the variable increases. That's the sort of thing that's meant here.