At some point, you neglect infinitesimals. The notion of equality changes from something exact to something that's infinitely close.
February 7, 2026 at 5:25 PM
At some point, you neglect infinitesimals. The notion of equality changes from something exact to something that's infinitely close.
🙏You should see the indecent ones. ME. Big enough to qualify as a primitive backwoods Airbnb. Maybe 450 to 550 pots between its two chambers (there's a catenary arch for soda instead of a sutema), depending. I worked out the cu. ft. with metric tensors and infinitesimals but then forgot the solution
February 2, 2026 at 12:33 PM
🙏You should see the indecent ones. ME. Big enough to qualify as a primitive backwoods Airbnb. Maybe 450 to 550 pots between its two chambers (there's a catenary arch for soda instead of a sutema), depending. I worked out the cu. ft. with metric tensors and infinitesimals but then forgot the solution
But at great cost she now shambles towards Bethlehem, negotiating the last infinitesimals between three layers of active and resolved activity slowly aligning itself with a terrified body that's learning how to integrate
But this is a homecoming, and all parts know it, and now we see how confused
But this is a homecoming, and all parts know it, and now we see how confused
February 1, 2026 at 7:36 PM
But at great cost she now shambles towards Bethlehem, negotiating the last infinitesimals between three layers of active and resolved activity slowly aligning itself with a terrified body that's learning how to integrate
But this is a homecoming, and all parts know it, and now we see how confused
But this is a homecoming, and all parts know it, and now we see how confused
I have just come to appreciate that one can come to appreciate that being art low means one has an entire new world to explore between the infinitesimals
Pull the lip back just so, now draw the back of the tongue up and forward, just below the back of the palate. Congruency of tongue and lips
Pull the lip back just so, now draw the back of the tongue up and forward, just below the back of the palate. Congruency of tongue and lips
February 1, 2026 at 6:21 PM
I have just come to appreciate that one can come to appreciate that being art low means one has an entire new world to explore between the infinitesimals
Pull the lip back just so, now draw the back of the tongue up and forward, just below the back of the palate. Congruency of tongue and lips
Pull the lip back just so, now draw the back of the tongue up and forward, just below the back of the palate. Congruency of tongue and lips
Nope, I asked my mutlivariate prof to give me rigorous explanation of infinitesimals and after trying to understand Cauchy I knew it was my last math class.
January 31, 2026 at 4:27 AM
Nope, I asked my mutlivariate prof to give me rigorous explanation of infinitesimals and after trying to understand Cauchy I knew it was my last math class.
Honestly reminds me so much of Archimedes work with infinitesimals
Namely, Oresme drew graphs as below and "applied this concept to the analysis of local motion where the latitudo or intensity represented the speed, the longitudo represented the time, and the area of the figure represented the distance travelled".
(2/2)
(2/2)
January 28, 2026 at 9:53 PM
Honestly reminds me so much of Archimedes work with infinitesimals
girl whose knowledge of math is approximately 7th-grade level voice: does nonstandard analysis here mean that calculus of infinitesimals, as contrasted with the calculus of limits?
January 26, 2026 at 8:53 AM
girl whose knowledge of math is approximately 7th-grade level voice: does nonstandard analysis here mean that calculus of infinitesimals, as contrasted with the calculus of limits?
Speaking of encyclopediæ, it amuses me that there are whole paragraphs in Wikipedia on why many students cannot grasp that 0.999… (aka 0.999 recurring) is exactly equal to one.
January 21, 2026 at 6:32 AM
Speaking of encyclopediæ, it amuses me that there are whole paragraphs in Wikipedia on why many students cannot grasp that 0.999… (aka 0.999 recurring) is exactly equal to one.
Imagine where we would be today if the Ancient Greeks had just accepted that infinitesimals exist...
January 16, 2026 at 3:35 PM
Imagine where we would be today if the Ancient Greeks had just accepted that infinitesimals exist...
In Althea and the Mysteries of Calculus (ch13), Mom is doing a proof using infinitesimals. The kids feel like it shows them more. That's what got me thinking about this. (Writing this book has gotten me to think about and learn quite a bit.)
January 12, 2026 at 10:57 PM
In Althea and the Mysteries of Calculus (ch13), Mom is doing a proof using infinitesimals. The kids feel like it shows them more. That's what got me thinking about this. (Writing this book has gotten me to think about and learn quite a bit.)
I am obsessed
with continuity
Infinitesimals
and the arbitrarily large
avatars of the tortoise
the third man and his infinite shadow
the volumes of Euler...
with continuity
Infinitesimals
and the arbitrarily large
avatars of the tortoise
the third man and his infinite shadow
the volumes of Euler...
January 10, 2026 at 4:59 AM
I am obsessed
with continuity
Infinitesimals
and the arbitrarily large
avatars of the tortoise
the third man and his infinite shadow
the volumes of Euler...
with continuity
Infinitesimals
and the arbitrarily large
avatars of the tortoise
the third man and his infinite shadow
the volumes of Euler...
Hey engineers... Hate working with limits?
Pick a topos with a line object and define an infinitesimals object as a subobject of it. You'll never need limits again.
Glad I could help!
Pick a topos with a line object and define an infinitesimals object as a subobject of it. You'll never need limits again.
Glad I could help!
January 5, 2026 at 1:29 AM
Hey engineers... Hate working with limits?
Pick a topos with a line object and define an infinitesimals object as a subobject of it. You'll never need limits again.
Glad I could help!
Pick a topos with a line object and define an infinitesimals object as a subobject of it. You'll never need limits again.
Glad I could help!
Math Sky, I just learned about Robinson's infinitesimals and I am shook, just shook to learn that you can do calculus entirely without taking limits. Newton and Leibniz were right, they just couldn't prove it.
January 2, 2026 at 8:02 PM
Math Sky, I just learned about Robinson's infinitesimals and I am shook, just shook to learn that you can do calculus entirely without taking limits. Newton and Leibniz were right, they just couldn't prove it.
"The happiness of life is made up of minute fractions: the soon forgotten charities, a smile, a kind look, a heartfelt compliment, the countless infinitesimals of pleasurable and genial feeling." Samuel Taylor Coleridge. "To have joy one must share it--happiness was born a twin." Lord Byron.
December 29, 2025 at 11:22 AM
"The happiness of life is made up of minute fractions: the soon forgotten charities, a smile, a kind look, a heartfelt compliment, the countless infinitesimals of pleasurable and genial feeling." Samuel Taylor Coleridge. "To have joy one must share it--happiness was born a twin." Lord Byron.
#iTeachMath ♾️
For fans of non-standard analysis:
In Althea and the Mysteries of Calculus, I hope to use the simplest possible proofs. Some use limits, others use infinitesimals. As much as possible, I'd like to use infinitesimals.
Email me at [email protected] if interested.
For fans of non-standard analysis:
In Althea and the Mysteries of Calculus, I hope to use the simplest possible proofs. Some use limits, others use infinitesimals. As much as possible, I'd like to use infinitesimals.
Email me at [email protected] if interested.
December 28, 2025 at 6:01 AM
#iTeachMath ♾️
For fans of non-standard analysis:
In Althea and the Mysteries of Calculus, I hope to use the simplest possible proofs. Some use limits, others use infinitesimals. As much as possible, I'd like to use infinitesimals.
Email me at [email protected] if interested.
For fans of non-standard analysis:
In Althea and the Mysteries of Calculus, I hope to use the simplest possible proofs. Some use limits, others use infinitesimals. As much as possible, I'd like to use infinitesimals.
Email me at [email protected] if interested.
Leibniz ranting about infinitesimals
December 24, 2025 at 5:10 PM
Leibniz ranting about infinitesimals
Curious what happens when a student in a calculus class says they don't believe in infinitesimals.
December 24, 2025 at 3:29 PM
Curious what happens when a student in a calculus class says they don't believe in infinitesimals.
"The happiness of life is made up of minute fractions—the little soon-forgotten charities of a kiss, a smile, a kind look, a heartfelt compliment in the disguise of a playful raillery, and the countless other infinitesimals of pleasurable thought and genial feeling."
~~Samuel Taylor Coleridge
.
~~Samuel Taylor Coleridge
.
December 20, 2025 at 7:33 PM
"The happiness of life is made up of minute fractions—the little soon-forgotten charities of a kiss, a smile, a kind look, a heartfelt compliment in the disguise of a playful raillery, and the countless other infinitesimals of pleasurable thought and genial feeling."
~~Samuel Taylor Coleridge
.
~~Samuel Taylor Coleridge
.
A Comparative Framework: Planck Time, Infinitesimals, and the Nature of Geodesics
beyondturbulence.blogspot.com/2025/12/a-co...
beyondturbulence.blogspot.com/2025/12/a-co...
A Comparative Framework: Planck Time, Infinitesimals, and the Nature of Geodesics
Coach . Taj . Intention . Lisp . turbulence . intelligence . tj-coulon . troy . beyond . allusive . p-vs-np . Pure . Musical . Visual . Direct .
beyondturbulence.blogspot.com
December 16, 2025 at 8:54 PM
A Comparative Framework: Planck Time, Infinitesimals, and the Nature of Geodesics
beyondturbulence.blogspot.com/2025/12/a-co...
beyondturbulence.blogspot.com/2025/12/a-co...
*the manipulation of infinitesimals can actually be made rigorous by using something like measure theory (iirc) or another vaguely similar theory as a foundation for the definition thereof
November 24, 2025 at 1:37 AM
*the manipulation of infinitesimals can actually be made rigorous by using something like measure theory (iirc) or another vaguely similar theory as a foundation for the definition thereof
...for f'(x)=g(f(x)), it's quite easy to get a non-differential form by rearranging to f'(x)/g(f(x)), integrating with a u-sub of u=f(x) (or equivalently manipulating infinitesimals to get df/g(f) = dx and integrating ∫df/g(f) = ∫dx*) which gives h(f(x))=x+C, where h(y)=∫dy/g(y). This then solves...
November 24, 2025 at 1:37 AM
...for f'(x)=g(f(x)), it's quite easy to get a non-differential form by rearranging to f'(x)/g(f(x)), integrating with a u-sub of u=f(x) (or equivalently manipulating infinitesimals to get df/g(f) = dx and integrating ∫df/g(f) = ∫dx*) which gives h(f(x))=x+C, where h(y)=∫dy/g(y). This then solves...
That won't make this math teacher cry (if it's done correctly). Think in terms of infinitesimals. They really are fine.
November 22, 2025 at 8:56 PM
That won't make this math teacher cry (if it's done correctly). Think in terms of infinitesimals. They really are fine.
As we have a Cantor for infinities do we need a Cantor for zeroes? Approaching zero, infinitesimals, decimals and multiples of ten. What happens when we move from minus one to plus one? Is it complex? What does quantum foam tell us about zero?
November 22, 2025 at 4:11 PM
As we have a Cantor for infinities do we need a Cantor for zeroes? Approaching zero, infinitesimals, decimals and multiples of ten. What happens when we move from minus one to plus one? Is it complex? What does quantum foam tell us about zero?
The happiness of life is made up of minute fractions -the little, soon forgotten charities of a kiss or smile, a kind look, a heartfelt compliment, and the countless infinitesimals of pleasurable and genial feeling.
Samuel Taylor Coleridge
English Poet
(by app Quoteee)
#booksky #quotes #motivation
Samuel Taylor Coleridge
English Poet
(by app Quoteee)
#booksky #quotes #motivation
November 17, 2025 at 9:08 PM
The happiness of life is made up of minute fractions -the little, soon forgotten charities of a kiss or smile, a kind look, a heartfelt compliment, and the countless infinitesimals of pleasurable and genial feeling.
Samuel Taylor Coleridge
English Poet
(by app Quoteee)
#booksky #quotes #motivation
Samuel Taylor Coleridge
English Poet
(by app Quoteee)
#booksky #quotes #motivation
One of the Discovery Institute people wrote a history of calculus, I never bothered to read it but apparently infinitesimals were allowed.
November 16, 2025 at 7:59 PM
One of the Discovery Institute people wrote a history of calculus, I never bothered to read it but apparently infinitesimals were allowed.