Expert answers to "Why does a nontrivial V → V have..." - Plainmath

Maverick Avery

Answered question

2022-10-28

Why does a nontrivial

V \to V

have a critical point?

Answer & Explanation

spornya1

Beginner2022-10-29Added 18 answers

First of all, by elementarity

rank (j (x)) = j (rank (x))

. So it suffices to show that there is some

x

whose rank is moved.
Now we can prove the following by induction:
Suppose that

rank (j (x)) = rank (x)

and for all

y

such that

rank (y) < rank (x)

,

j (y) = y

, then

j (x) = x

.
Simply note that

y \in x \leftrightarrow j (y) \in j (x) \leftrightarrow y \in j (x)

.

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Differential Calculus

What is the Mixed Derivative Theorem for mixed second-order partial derivatives? How can it help in calculating partial derivatives of second and higher orders?
How do I find the y-intercept of a parabola?
What are the vertices of $9 x^{2} + 16 y^{2} = 144$ ?
How to determine the rate of change of a function?
Why are the tangents for 90 and 270 degrees undefined?
How to find the center and radius of the circle $x^{2} + y^{2} - 6 x + 8 y = 0$ ?
What is multiplicative inverse of a number?
How to find the continuity of a function on a closed interval?
How do I find the tangent line of a function?
How to find vertical asymptotes using limits?
How to find the center and radius of the circle $x^{2} - 12 x + y^{2} + 4 y + 15 = 0$ ?
Let f be a function so that (below). Which must be true?
I. f is continuous at x=2
II. f is differentiable at x=2
III. The derivative of f is continuous at x=2
(A) I (B) II (C) I and II (D) I and III (E) II and III
How to find the center and radius of the circle given $x^{2} + y^{2} + 8 x - 6 y = 0$ ?
How to find the center and radius of the circle $x^{2} + y^{2} + 4 x - 8 y + 4 = 0$ ?
How to identify the center and radius of the circle ${(x + 3)}^{2} + {(y - 8)}^{2} = 16$ ?

Didn't find what you were looking for?