Reminds me of a problem, back in the 1970s. Nobody in class could even get started, because it use the term "Parallelepiped" and nobody knew what that was.
I was aware that a parabola was defined as the set of points equidistant between a point and a line. Not knowing what a "fixed point" was, and seeing the formula of a parabola, I was suspecting the question could be rephrased "What point defines this parabola?" Boy, was I wrong!
f(x)=xⁿ , n∈N For the fixed points then, xⁿ=x x(xⁿ⁻¹-1)=0 And Then, x=0 or xⁿ⁻¹=1 then we can conclude if f(x)=xⁿ Its fixed points will be (0,0) and (1,1) if n is even. And (0,0), (1,1), and (-1,-1) if n is odd.
x=0 and x=1. No video needed. Just asked yourself, which number or numbers, if any, can you raise to a power and get back the same number. 0 to any power (except 0) is 0 and 1 to any power is 1.
This is the first time I am even hearing the term "fixed point", and I used to be a centurion in mathematics during my school days. Thank you very much! P.S. Centurion = someone who consistently scores 100% in the exams
I heard it has a lot to do with Real Analysis, but now i struggle with proof exercises. Sometimes when stuck, I don't know if it's the time to look for the answer. Advice, anyone?
Reminds me of a problem, back in the 1970s.
Nobody in class could even get started, because it use the term "Parallelepiped" and nobody knew what that was.
A new thing enters my knowledge. Thank you very very much.❤
I am a young kid and i can understand really hard math and this channel is very helpful keep up your work! Amazing
0:45 I am just wondering what kind of math he will teach us when Doom music kicks in.
thanks so much i wont stop learning
I was aware that a parabola was defined as the set of points equidistant between a point and a line. Not knowing what a "fixed point" was, and seeing the formula of a parabola, I was suspecting the question could be rephrased "What point defines this parabola?" Boy, was I wrong!
Can you do the fixed points of f(x) = x^n? Would be an interesting video!
f(x)=xⁿ , n∈N
For the fixed points
then, xⁿ=x
x(xⁿ⁻¹-1)=0
And
Then, x=0 or xⁿ⁻¹=1
then we can conclude
if f(x)=xⁿ
Its fixed points will be
(0,0) and (1,1) if n is even.
And
(0,0), (1,1), and (-1,-1) if n is odd.
@@sajuvasu cool! Surely there are complex solutions too?
E@sajuvasu I think you just did his homework.
For real analysis, no complex solutions.
x=0 and x=1. No video needed. Just asked yourself, which number or numbers, if any, can you raise to a power and get back the same number. 0 to any power (except 0) is 0 and 1 to any power is 1.
At first after viewing the question, I thought it asks for the point where f(x) is at its minimum or maximum.
thanks :)
This is the first time I am even hearing the term "fixed point", and I used to be a centurion in mathematics during my school days. Thank you very much!
P.S. Centurion = someone who consistently scores 100% in the exams
I heard it has a lot to do with Real Analysis, but now i struggle with proof exercises. Sometimes when stuck, I don't know if it's the time to look for the answer. Advice, anyone?
Try not to look at the answer. Think about it for a few days and eventually YOU will figure it out. That is how you learn math.
I just gained 10 IQ points.
asnwer=1 isit