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Oct 26, 2021 at 8:43 comment added MBN This is the definition of a tangent vector at a given point $p$. The point is fixed, that's why it is missing from the notation.
Oct 26, 2021 at 6:00 history tweeted twitter.com/StackPhysics/status/1452877666915438593
Oct 25, 2021 at 22:00 history became hot network question
S Oct 25, 2021 at 15:00 vote accept Egg Man
Oct 25, 2021 at 14:54 vote accept Egg Man
S Oct 25, 2021 at 15:00
Oct 25, 2021 at 14:52 answer added Slereah timeline score: 5
Oct 25, 2021 at 14:44 comment added WillO In elementary calculus, we teach students that the derivative of a function (at a particular point) is a number. Later on, we teach them that it is a function, taking as input the point at which you differentiated. Same thing here: A tangent vector (at a particular point) takes a function and returns a number. A collection of tangent vectors, one for each point, takes a function and gives you a function that takes the point as input. Such a collection of tangent vectors, if it varies continuously (or differentiably) is called a continuous (or differentiable) vector field.
Oct 25, 2021 at 14:37 answer added user1379857 timeline score: 3
Oct 25, 2021 at 14:29 history edited Qmechanic
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Oct 25, 2021 at 14:05 history edited Egg Man CC BY-SA 4.0
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Oct 25, 2021 at 14:00 history asked Egg Man CC BY-SA 4.0