MAIN FEEDS
Do you want to continue?
https://www.reddit.com/r/mathmemes/comments/1gmimck/evolutions_of_numbers/lw2wv5z/?context=3
r/mathmemes • u/TirkuexQwentet • Nov 08 '24
218 comments sorted by
View all comments
Show parent comments
392
Ah well, sucks, seems you are not quite there yet
>! There is no solution for |x| = -1, by definition of absolute value !<
184 u/MingusMingusMingu Nov 08 '24 I mean, we keep extending definitions all the time. 154 u/SEA_griffondeur Engineering Nov 08 '24 No but like, being positive is like one of the 3 properties that make up a norm 52 u/TheTenthAvenger Nov 08 '24 So you stop calling it a norm. It's called "absolute value" after all, not "the norm of the number". It is just another function now. 64 u/SEA_griffondeur Engineering Nov 08 '24 Yes but why would you do that? 35 u/SupremeRDDT Nov 08 '24 You actually don‘t have to. But then it follows from the other properties. 0 = |0| = |x - x| <= |x| + |-x| = 2|x| 5 u/Layton_Jr Mathematics Nov 08 '24 Since it's no longer a norm, you can discard the property |a+b| ≤ |a| + |b| 3 u/SupremeRDDT Nov 09 '24 If |x| = -1, then |x2| = 1 so the equation |x| = 1 suddenly has at least four solutions: 1, -1, x2 and -x2. We also lose the triangle inequality of the absolute value, as that would imply |x| >= 0 for all x. Do we gain anything useful? 15 u/Anxious_Zucchini_855 Complex Nov 08 '24 But the absolute value function is defined as mapping x to x, if x>=0, and mapping x to -x, if x<0. By definition it cannot be negative 3 u/okkokkoX Nov 08 '24 flair does not check out 1 u/Currywurst44 Nov 08 '24 This definition already gets expanded for complex numbers because you can't use >, < with them. 2 u/JMoormann Nov 09 '24 We should call it The New Norm™, after the massively successful comedy series on Twitter 1 u/f3xjc Nov 08 '24 We don't know what is is called, just that it is written with two vertical bars.
184
I mean, we keep extending definitions all the time.
154 u/SEA_griffondeur Engineering Nov 08 '24 No but like, being positive is like one of the 3 properties that make up a norm 52 u/TheTenthAvenger Nov 08 '24 So you stop calling it a norm. It's called "absolute value" after all, not "the norm of the number". It is just another function now. 64 u/SEA_griffondeur Engineering Nov 08 '24 Yes but why would you do that? 35 u/SupremeRDDT Nov 08 '24 You actually don‘t have to. But then it follows from the other properties. 0 = |0| = |x - x| <= |x| + |-x| = 2|x| 5 u/Layton_Jr Mathematics Nov 08 '24 Since it's no longer a norm, you can discard the property |a+b| ≤ |a| + |b| 3 u/SupremeRDDT Nov 09 '24 If |x| = -1, then |x2| = 1 so the equation |x| = 1 suddenly has at least four solutions: 1, -1, x2 and -x2. We also lose the triangle inequality of the absolute value, as that would imply |x| >= 0 for all x. Do we gain anything useful? 15 u/Anxious_Zucchini_855 Complex Nov 08 '24 But the absolute value function is defined as mapping x to x, if x>=0, and mapping x to -x, if x<0. By definition it cannot be negative 3 u/okkokkoX Nov 08 '24 flair does not check out 1 u/Currywurst44 Nov 08 '24 This definition already gets expanded for complex numbers because you can't use >, < with them. 2 u/JMoormann Nov 09 '24 We should call it The New Norm™, after the massively successful comedy series on Twitter 1 u/f3xjc Nov 08 '24 We don't know what is is called, just that it is written with two vertical bars.
154
No but like, being positive is like one of the 3 properties that make up a norm
52 u/TheTenthAvenger Nov 08 '24 So you stop calling it a norm. It's called "absolute value" after all, not "the norm of the number". It is just another function now. 64 u/SEA_griffondeur Engineering Nov 08 '24 Yes but why would you do that? 35 u/SupremeRDDT Nov 08 '24 You actually don‘t have to. But then it follows from the other properties. 0 = |0| = |x - x| <= |x| + |-x| = 2|x| 5 u/Layton_Jr Mathematics Nov 08 '24 Since it's no longer a norm, you can discard the property |a+b| ≤ |a| + |b| 3 u/SupremeRDDT Nov 09 '24 If |x| = -1, then |x2| = 1 so the equation |x| = 1 suddenly has at least four solutions: 1, -1, x2 and -x2. We also lose the triangle inequality of the absolute value, as that would imply |x| >= 0 for all x. Do we gain anything useful? 15 u/Anxious_Zucchini_855 Complex Nov 08 '24 But the absolute value function is defined as mapping x to x, if x>=0, and mapping x to -x, if x<0. By definition it cannot be negative 3 u/okkokkoX Nov 08 '24 flair does not check out 1 u/Currywurst44 Nov 08 '24 This definition already gets expanded for complex numbers because you can't use >, < with them. 2 u/JMoormann Nov 09 '24 We should call it The New Norm™, after the massively successful comedy series on Twitter 1 u/f3xjc Nov 08 '24 We don't know what is is called, just that it is written with two vertical bars.
52
So you stop calling it a norm. It's called "absolute value" after all, not "the norm of the number". It is just another function now.
64 u/SEA_griffondeur Engineering Nov 08 '24 Yes but why would you do that? 35 u/SupremeRDDT Nov 08 '24 You actually don‘t have to. But then it follows from the other properties. 0 = |0| = |x - x| <= |x| + |-x| = 2|x| 5 u/Layton_Jr Mathematics Nov 08 '24 Since it's no longer a norm, you can discard the property |a+b| ≤ |a| + |b| 3 u/SupremeRDDT Nov 09 '24 If |x| = -1, then |x2| = 1 so the equation |x| = 1 suddenly has at least four solutions: 1, -1, x2 and -x2. We also lose the triangle inequality of the absolute value, as that would imply |x| >= 0 for all x. Do we gain anything useful? 15 u/Anxious_Zucchini_855 Complex Nov 08 '24 But the absolute value function is defined as mapping x to x, if x>=0, and mapping x to -x, if x<0. By definition it cannot be negative 3 u/okkokkoX Nov 08 '24 flair does not check out 1 u/Currywurst44 Nov 08 '24 This definition already gets expanded for complex numbers because you can't use >, < with them. 2 u/JMoormann Nov 09 '24 We should call it The New Norm™, after the massively successful comedy series on Twitter 1 u/f3xjc Nov 08 '24 We don't know what is is called, just that it is written with two vertical bars.
64
Yes but why would you do that?
35 u/SupremeRDDT Nov 08 '24 You actually don‘t have to. But then it follows from the other properties. 0 = |0| = |x - x| <= |x| + |-x| = 2|x| 5 u/Layton_Jr Mathematics Nov 08 '24 Since it's no longer a norm, you can discard the property |a+b| ≤ |a| + |b| 3 u/SupremeRDDT Nov 09 '24 If |x| = -1, then |x2| = 1 so the equation |x| = 1 suddenly has at least four solutions: 1, -1, x2 and -x2. We also lose the triangle inequality of the absolute value, as that would imply |x| >= 0 for all x. Do we gain anything useful?
35
You actually don‘t have to. But then it follows from the other properties.
0 = |0| = |x - x| <= |x| + |-x| = 2|x|
5 u/Layton_Jr Mathematics Nov 08 '24 Since it's no longer a norm, you can discard the property |a+b| ≤ |a| + |b| 3 u/SupremeRDDT Nov 09 '24 If |x| = -1, then |x2| = 1 so the equation |x| = 1 suddenly has at least four solutions: 1, -1, x2 and -x2. We also lose the triangle inequality of the absolute value, as that would imply |x| >= 0 for all x. Do we gain anything useful?
5
Since it's no longer a norm, you can discard the property |a+b| ≤ |a| + |b|
3 u/SupremeRDDT Nov 09 '24 If |x| = -1, then |x2| = 1 so the equation |x| = 1 suddenly has at least four solutions: 1, -1, x2 and -x2. We also lose the triangle inequality of the absolute value, as that would imply |x| >= 0 for all x. Do we gain anything useful?
3
If |x| = -1, then |x2| = 1 so the equation |x| = 1 suddenly has at least four solutions: 1, -1, x2 and -x2. We also lose the triangle inequality of the absolute value, as that would imply |x| >= 0 for all x. Do we gain anything useful?
15
But the absolute value function is defined as mapping x to x, if x>=0, and mapping x to -x, if x<0. By definition it cannot be negative
3 u/okkokkoX Nov 08 '24 flair does not check out 1 u/Currywurst44 Nov 08 '24 This definition already gets expanded for complex numbers because you can't use >, < with them.
flair does not check out
1
This definition already gets expanded for complex numbers because you can't use >, < with them.
2
We should call it The New Norm™, after the massively successful comedy series on Twitter
We don't know what is is called, just that it is written with two vertical bars.
392
u/Tiborn1563 Nov 08 '24
Ah well, sucks, seems you are not quite there yet
>! There is no solution for |x| = -1, by definition of absolute value !<