In just a few minutes, we show the exact meaning of infinity itself within the context of calculus. This teaser shows just one pivotal concept of calculus that is often seen as nebulous or fuzzy by calculus students (we'll later see others, such as indeterminacy, limits, etc.)—all of these can be made extremely clear and precise by using the right pictures.
Some readers might find themselves resisting all of this initially, and we welcome feedback; our goal will be to make believers of everyone that takes the time to watch, listen, think, and question what is said here. As a first step, our next video will peek ahead to a few definitions from calculus as evidence that near-numbers are logically well-founded.
A quick disclaimer about what this video is not about. First, in interval notation such as (0,∞), the infinity symbol simply means that the interval has no end, which is not subtle and has nothing to do with calculus. Second, for anyone familiar with the "extended real line," our +∞ would be expressed as ∞-, squeezing toward ∞ from the left side; this extended real line is not well-suited for calculus, as we no longer have arithmetic working as it should there and it does not help to clarify calculus.
Some readers might find themselves resisting all of this initially, and we welcome feedback; our goal will be to make believers of everyone that takes the time to watch, listen, think, and question what is said here. As a first step, our next video will peek ahead to a few definitions from calculus as evidence that near-numbers are logically well-founded.
A quick disclaimer about what this video is not about. First, in interval notation such as (0,∞), the infinity symbol simply means that the interval has no end, which is not subtle and has nothing to do with calculus. Second, for anyone familiar with the "extended real line," our +∞ would be expressed as ∞-, squeezing toward ∞ from the left side; this extended real line is not well-suited for calculus, as we no longer have arithmetic working as it should there and it does not help to clarify calculus.
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