Is dlπ/2 equivalent to dl/(dlπ/2)?

In summary, the question is about the relationship between two infinitesimal lengths, dl and dlπ/2, and whether they are equal or equivalent. The conversation discusses how the two lengths are not equal, but are of the same order since they are both linearly dependent on dl. However, the book states that they are not equivalent.
  • #1
LCSphysicist
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Homework Statement
Is equivalent the infinitesimal segment and the semicircle with diameter equal to this infinitesimal segment?
Relevant Equations
l/(lpi/2)
dl = Infinitesimal length of the segment.
dlπ/2 = the semicircle length

lim dl-> zero
dl/(dlπ/2) = 2/π, no zero, so the answer would be yes.

But second the book, the answer is no, where am i wrong?
 
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  • #2
I see, actually I mistook same order and equivalence...
 
  • #3
Not sure what you mean by equivalent but they are not equal, they are two different infinitesimals, one is ##dx=dl## and the other is ##dy= \frac{\pi}{2}dx=\frac{\pi}{2}dl##.

They are of the same order as you say, they are both linearly dependent on dl so you might say that in this sense they are equivalent.
 

Related to Is dlπ/2 equivalent to dl/(dlπ/2)?

1. What are infinitesimals equivalents?

Infinitesimals equivalents are mathematical concepts that represent quantities that are infinitely small. They are used in calculus to help describe and analyze continuously changing systems.

2. How are infinitesimals equivalents used in calculus?

In calculus, infinitesimals equivalents are used to represent the change in a function over an infinitely small interval. This allows for more accurate and precise calculations and analysis of continuously changing systems.

3. Are infinitesimals equivalents the same as zero?

No, infinitesimals equivalents are not the same as zero. While they both represent small quantities, infinitesimals are considered to be non-zero and have a defined value, whereas zero has no value.

4. Can infinitesimals equivalents be used in real-world applications?

Yes, infinitesimals equivalents are used in many real-world applications, such as physics, engineering, and economics. They are particularly useful in modeling and predicting the behavior of continuously changing systems.

5. Are infinitesimals equivalents accepted by all mathematicians?

No, there is still debate among mathematicians about the validity of infinitesimals equivalents. Some mathematicians believe that they provide a useful tool for solving problems, while others argue that they are not well-defined and can lead to contradictions in mathematical reasoning.

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