in college we named that "extended projection" as the alexandroff compactification. and also you can make compact any non comapct set by adding the infinity element. cool to see this back. No idea what a wheel algebra is, maybe on my math degree was called something different too
What I like about the extended protection is how it makes lines in space into extremely wide circles that pass though the point infinity. It's very neat.
Sitting in my freshman math class, I came up with this projection concept but I had no idea this existed. My approach was evaluating how complex numbers would work with this creating a spherical or torrid geometry. The curvature would be flat because the number line extends to infinity. In other words, this concept as a "number line" would be the same for finite ranges.
fun fact: with floating point numbers, 1/0 is actually infinity, and 1/-0 is actually negative infinity. this is a byproduct of the fact that the number system is unable to truly represent 0 or inifity, only arbitrarily small and arbitrarily large numbers respectively
It seems to me that both the first and second conventional arithmetic problems with division by zero result from the implicit assumption that 0/0 = 1, thus allowing cancellation. If 0/0 = 0 instead, then all these problems seem to go away. For example 1/0 = x would no longer become 1 = x*0, as multiplying 1*(0/0) would result in 0 instead of, so it would just become 0 = x*0, which is unproblematic. In the example that seems to break equality entirely, 3*(0/0) = 5*(0/0) would just become 3*0 = 5*0, which also seems perfectly fine. Of course, 0/0 = 0 would still have to be justified beyond this, but I think that it can be done quite easily as follows: 0/0 = x (1/2)(0/0) = (1/2)x 0/0 = (1/2)x by simply fractional multiplication x = (1/2)x 2x = x 2x - x = 0 x = 0 Interestingly a similar process can be applied with any numerator over 0, resulting in a/0 = 0 for all values of a, for real numbers at least. You would have to accept that approaching 0 as a limit has nothing to do with the result, but something like f(x) = 1/x is already obviously non-continuous so I don't see that as much of a problem if I'm being honest.. I've been trying to poke holes in this idea for a few weeks now, but haven't found any that did not implicitly assume things about division by zero other than a/0 = 0.
7:56 infinity = in-fin-ity, a.k.a. just that which doesn’t have an end, or the non-finite-ness. +inf and -inf are equally non-finite so it kind of makes sense for the term to just cover both
The "What you learned is all a lie" shows the root problem in education: a teaching-sequence that necessitates the teaching of "lies" so that the next topic can be taught. My personal perception of the case for maths is that NEVER is the concept even mentioned that numbers (and formulas!) are REPRESENTATIONS of values. For instance the statement: 1 + 1 = 3 is mathematically True. Which should become obvious when one adds: for sufficiently large values of '1' because one then should see that each 'number' REPRESENTS a rounded-off VALUE. The NOT teaching of this representation thing causes the so-typical and unnecessary confusion.
Wont infinity plus infinity equal 0? For the first infinity, it goes halfway on the circle cimcurrfrrence. When the second infinity is added, it will travel another half and arrive back at 0. This works with substraction too, just in the opposite direction.
Question, if the 6 exceptions apply, are algebraic concepts not applyable? Like for example 6) if x/0=inf then inf*0=x, but we defined that inf*0 is undefined? How does that case get handeled? Amazing Video as always Edit: nvm watched the next videos and realized we not only broke that thingy lol
@@ValkyRiver yea thats what I figured. I edited the comment because in the next video all the other broken laws were shown. Left the comment here because I thougt its a fun thougt
Because it defies mathematics. Let’s say infinity - infinity equal zero. Now add one to both sides. infinity - infinity + 1 = 1. Since infinity plus any number is still infinity, simplify. Infinity - infinity = 1. This works for any number and just doesn’t make any sense. The weird thing about using 0 and infinity is that they can equal different things depending on what kind of math you are doing.
Why didn't you delay the other 2 videos by like 2 days? 3 videos all at the same time is kinda overwhelming. I don't mind waiting 2 days, infact, it's probably better since it gives me time to process the information you just gave me
I dunno man ....this idea of extended projection does not make sense..... doesn't this apply that if u go really really far to the left or right on the number line....u'll just end up on point 0....😰
No because no matter how high you go, you can only go up to infinity. It just really depends on what kind of math you are doing. What’s also kind of weird is how temperatures work. We know that 0 kelvin is the coldest anything can be, but what’s even more interesting is that infinite positive temperature isn’t the highest a temperature can get, negative temperatures are hotter. Going coldest to hottest, 0 kelvin, infinite kelvin, -infinite kelvin, -0 kelvin. It sounds really weird but it’s an actual real thing, and it fixes some problems which would break the law of thermodynamics.
@@leob69 that is very true i guess my brain invented something when i learned fractions, going by the way fractions were taught 2 slices in bread splits the bread up into thirds so dividing by 0 would mean -1 slices if we follow a pattern... 1/3 2 slices, 1/4 3 slices, 1/0 -1 slice. third grade logic does not win unfortunately :(
There are many proofs for this, but here's one that I can remember: Let x = 0.99999999..., or x=0.[9], where square brackets ([]) represent repeating digits. Multiply x by 10 to get 10x = 9.[9]. Since 9 repeats forever, multiplying by 10 would still result in repetition. Subtract x from 10x to get 9x = 9. The rest is obvious (9/9 = 1).
Your pacing, narration, animations, and corney comedic timing are almost as wonderful as the math topics you cover. Thanks for all the wonderful work.
I love your videos
in college we named that "extended projection" as the alexandroff compactification. and also you can make compact any non comapct set by adding the infinity element. cool to see this back. No idea what a wheel algebra is, maybe on my math degree was called something different too
What I like about the extended protection is how it makes lines in space into extremely wide circles that pass though the point infinity. It's very neat.
Love your approach! Thank you for sharing!!
Sitting in my freshman math class, I came up with this projection concept but I had no idea this existed. My approach was evaluating how complex numbers would work with this creating a spherical or torrid geometry. The curvature would be flat because the number line extends to infinity. In other words, this concept as a "number line" would be the same for finite ranges.
fun fact: with floating point numbers, 1/0 is actually infinity, and 1/-0 is actually negative infinity. this is a byproduct of the fact that the number system is unable to truly represent 0 or inifity, only arbitrarily small and arbitrarily large numbers respectively
Floating point numbers can represent both zero and infinity. Not sure what you mean by this
I love when you post new videos because they are always interesting
It seems to me that both the first and second conventional arithmetic problems with division by zero result from the implicit assumption that 0/0 = 1, thus allowing cancellation. If 0/0 = 0 instead, then all these problems seem to go away.
For example 1/0 = x would no longer become 1 = x*0, as multiplying 1*(0/0) would result in 0 instead of, so it would just become 0 = x*0, which is unproblematic.
In the example that seems to break equality entirely, 3*(0/0) = 5*(0/0) would just become 3*0 = 5*0, which also seems perfectly fine.
Of course, 0/0 = 0 would still have to be justified beyond this, but I think that it can be done quite easily as follows:
0/0 = x
(1/2)(0/0) = (1/2)x
0/0 = (1/2)x by simply fractional multiplication
x = (1/2)x
2x = x
2x - x = 0
x = 0
Interestingly a similar process can be applied with any numerator over 0, resulting in a/0 = 0 for all values of a, for real numbers at least.
You would have to accept that approaching 0 as a limit has nothing to do with the result, but something like f(x) = 1/x is already obviously non-continuous so I don't see that as much of a problem if I'm being honest..
I've been trying to poke holes in this idea for a few weeks now, but haven't found any that did not implicitly assume things about division by zero other than a/0 = 0.
I think very similarly
why does the channel description say goodbye cruel world?
It changed from "I solve equations to escape the horrors of existence" to that after he uploaded this. Hope hes ok
@@robguthrie8897 I really hope this person wasn't on the s**cide forum, which was covered by tantacrul
@@nad2040I hope that too
@@robguthrie8897 When did it changed ? Is it after this video or before ?
1/0 has an identity crisis over it's sign, but 0/0 has an identity crisis over it's absolute value too
Every time I see a new video from this guy I just give a like and then I watch it lol
11:16... Infinity divided by infinity is 1. Infinity minus infinity equals 0. I have defined them with my magic 8 ball.
You have the potential to be the best
You can also divide by zero using the IEEE standard.
4:00 I did the exact same thing when I was 15 😅
These videos are the best! Good work!!
7:56 infinity = in-fin-ity, a.k.a. just that which doesn’t have an end, or the non-finite-ness. +inf and -inf are equally non-finite so it kind of makes sense for the term to just cover both
The "What you learned is all a lie" shows the root problem in education: a teaching-sequence that necessitates the teaching of "lies" so that the next topic can be taught. My personal perception of the case for maths is that NEVER is the concept even mentioned that numbers (and formulas!) are REPRESENTATIONS of values.
For instance the statement:
1 + 1 = 3
is mathematically True. Which should become obvious when one adds:
for sufficiently large values of '1'
because one then should see that each 'number' REPRESENTS a rounded-off VALUE.
The NOT teaching of this representation thing causes the so-typical and unnecessary confusion.
Amazing video
Wont infinity plus infinity equal 0? For the first infinity, it goes halfway on the circle cimcurrfrrence. When the second infinity is added, it will travel another half and arrive back at 0. This works with substraction too, just in the opposite direction.
Question, if the 6 exceptions apply, are algebraic concepts not applyable?
Like for example 6) if x/0=inf then inf*0=x, but we defined that inf*0 is undefined?
How does that case get handeled?
Amazing Video as always
Edit: nvm watched the next videos and realized we not only broke that thingy lol
x/0 = ∞
(x/0) * 0 = ∞ * 0
x * (0/0) = ∞
The *0 and /0 cannot cancel out, as 0/0 is indeterminate, not 1.
@@ValkyRiver yea thats what I figured. I edited the comment because in the next video all the other broken laws were shown. Left the comment here because I thougt its a fun thougt
can't wait to put my socks
pls come back
What? Is infinity minus infinity undefined? I thought it would be zero, I mean, I have done that to cancel out periodic repeating decimals.
Because it defies mathematics. Let’s say infinity - infinity equal zero. Now add one to both sides. infinity - infinity + 1 = 1. Since infinity plus any number is still infinity, simplify. Infinity - infinity = 1. This works for any number and just doesn’t make any sense. The weird thing about using 0 and infinity is that they can equal different things depending on what kind of math you are doing.
Infinite is a set of numbers but infinite numbers are not algebraic.
Ex: ...123123.123123... is an infinite number.
Love your videos
loyal
do more videos pls 😢👉👈
remember me when you become famous
There is an error, it says x-♾️=♾️, but x-♾️=-♾️
I like your videos; and I think 0 should equal infinity
When you made 3 videos and upload them all at once:
Why didn't you delay the other 2 videos by like 2 days? 3 videos all at the same time is kinda overwhelming. I don't mind waiting 2 days, infact, it's probably better since it gives me time to process the information you just gave me
Might not be the best for the algorithm, but I really like that I can binge all of them one after the other
3:35 so technically 2=5 with that logic (Lol no)
I dunno man ....this idea of extended projection does not make sense..... doesn't this apply that if u go really really far to the left or right on the number line....u'll just end up on point 0....😰
No because no matter how high you go, you can only go up to infinity. It just really depends on what kind of math you are doing. What’s also kind of weird is how temperatures work. We know that 0 kelvin is the coldest anything can be, but what’s even more interesting is that infinite positive temperature isn’t the highest a temperature can get, negative temperatures are hotter. Going coldest to hottest, 0 kelvin, infinite kelvin, -infinite kelvin, -0 kelvin. It sounds really weird but it’s an actual real thing, and it fixes some problems which would break the law of thermodynamics.
I used to think that anything divided by 0 is itself since you split it up 0 times but now...
with that argumentation, if you split it up 1 time, it would still be itself. How would x/0==x/1? But I get how it would make sense :D
@@leob69 that is very true i guess my brain invented something when i learned fractions, going by the way fractions were taught 2 slices in bread splits the bread up into thirds so dividing by 0 would mean -1 slices if we follow a pattern... 1/3 2 slices, 1/4 3 slices, 1/0 -1 slice. third grade logic does not win unfortunately :(
Why is 0.99999999... equal to 1?
There are many proofs for this, but here's one that I can remember:
Let x = 0.99999999..., or x=0.[9], where square brackets ([]) represent repeating digits.
Multiply x by 10 to get 10x = 9.[9]. Since 9 repeats forever, multiplying by 10 would still result in repetition.
Subtract x from 10x to get 9x = 9. The rest is obvious (9/9 = 1).
Well... it depends on what 0.99999999... refers to, and whether infinitesimals are allowed