(March 15, 2016 at 4:06 am)BrianSoddingBoru4 Wrote: two infinitesimals + two infinitesimals = four infinitesimals

Easy peasy.

Boru

You'd still get an infinitesimal; I guess that one would need to "sum" (integrate) an infinite number of infinitesimals to get a finite number?

(March 15, 2016 at 7:45 am)Jehanne Wrote:

(March 15, 2016 at 4:06 am)BrianSoddingBoru4 Wrote: two infinitesimals + two infinitesimals = four infinitesimals

Easy peasy.

Boru

You'd still get an infinitesimal; I guess that one would need to "sum" (integrate) an infinite number of infinitesimals to get a finite number?

That's pretty much what an integral is, yes.

(March 15, 2016 at 7:46 am)Alex K Wrote:

(March 15, 2016 at 7:45 am)Jehanne Wrote: You'd still get an infinitesimal; I guess that one would need to "sum" (integrate) an infinite number of infinitesimals to get a finite number?

That's pretty much what an integral is, yes.

Thanks; that makes the concept much clearer.  When I first took calculus 30 years ago, the class was not taught with infinitesimals; in fact, they weren't even mentioned.

(March 15, 2016 at 5:08 am)robvalue Wrote: Please let me know if what I've written isn't clear, and I'll do some diagrams or a video or something

Don't get WLC started.

(March 15, 2016 at 7:56 am)Jehanne Wrote:

(March 15, 2016 at 7:46 am)Alex K Wrote: That's pretty much what an integral is, yes.

Thanks; that makes the concept much clearer.  When I first took calculus 30 years ago, the class was not taught with infinitesimals; in fact, they weren't even mentioned.

Maybe not exactly in this form, on usually talks about Leibniz's differentials dx or whatever you want to call them. You must have used the Leibniz calculus df/dx and all that in differentiation and integration, right?

You're welcome

Calculus has a lot to do with limits of things approaching zero, both for differentiating and integrating.

For example, differentiating a function is done by [lim h tend to 0 ]( (f(x+h) - f(x)) / h )

You're calculating a tangent at a particular point by taking an approximate tangent extremely close by at the point x+h, and then allowing h to shrink right down to zero.

Maths has always been one of my passions!

Rob says "trapeziums", my mind goes to the Flying Wallendas and I hear calliope circus music in my head. (sigh)

Hehe.

Maybe it should be trapizii?

No! It's trapezia, apparently.

(March 15, 2016 at 8:47 am)robvalue Wrote: Hehe.

Maybe it should be trapizii?

No! It's trapezia, apparently.

Trapezoids, we Yanks say

Now those do sound like robot acrobats