True. Infinity is impossible for humans to understand because in reality infinity does not exist. There is no factual thing you can bind the mathematical term of infinity.
It works with any number not just with 1. So any number can be represented by having a finite decimal and with an infite recurrance. For example 2.999... = 3 and 42.2332999... = 42.2333.
Mathematics isn't flawed, it all adds up Everything in mathematics is proven with other mathematical equations.
Maybe it's just me then. For me it's easy to grasp concept of nothing or no offset.
I meant the concept. I for one can't imagine a infinite amount of anything. I can imagine none, one, half, two thirds, two, hundread million, ... I can even imagine a negative as a offset in a coordinate system. But not infinite.
This doesn't work, as the time halves with distance. It's not that he never reached the button, it's just that you never got far enough with your measurements to see him do it.
It's like watching a car approach a finish line, giving up before it reaches it and claiming that it never got any further than that point.
The offical result with divison with zero is undefined. The result closes to infinity the closer you get to zero, but division by exactly zero is not defined.
Actually a simple proof on the undefideness is that if you would expect that for example 3/0 = infinity, then infinity*0 = 3 which is not a true statement. Therefore the first statement is wrong.
I did indeed write it wrong, although mathematically the same value was derrived and what I wrote was correct - specifically, infinity/0 = 1 was highlighted as false.
This is why I'll never understand hardcore mathematics. As soon as the step is made from tangible numbers and figures to infinites and other intangible theories I'll lock up and start pondering on their existence instead of applying them. I guess the problem lies in the fact that I don't see maths as theory, but as something practical and tangible. Two systems of tangible and intangible numbers (which is one system if maths is just theory) collide and cause some sort of confusion for me. One plus one can be visually explained, whereas 1 + 0.9(9) cannot, or at least not afaik.
Interesting point of view. But 0 in a multiplication is always 0, so doesn't this then become a question like where the brackets are in a big algebra statement - ie: what numbers is more significant, 0 or infinity? I guess by that logic, 0.
Doesn't really matter because if infinity would be more significant the result would be inifinity and if 0 was the more significant the result would be 0. Neither of those are 3.
Which highlights you are right, but what if we state that because we substituted /0 for *infinity, we also substitute *0 for /infinity
So keeping are triple multiple of infinity, we divide by infinity:
(3*infinity)/infinity=3
Of course we could argue that 3*infinity=infinity and infinity/infinity=1 but isn't that simply missunderstanding the concept of infinity?
I think reasonably it depends on whether you want a division by 0 to break your sum or whether you wish to carry on processing it with infinities. If you can't handle the division by 0 then you are constrained and prevented from ever having to (as a programmer I can argue lots of cases where it would be good if computers could handle infinity as division by 0 sucks).
Rather than avoid the problem and say division by 0 is undefined, isn't it better to tackle it head on and simply consider infinity as an endless array? So that instead of hiding from an unsolveable puzzle, we simply handle the puzzle with a new concept - that of infinity.
Not in my opinion. Multiplying infinity with any number does not really matter because it will still be infinite. Also infinity/infinity probably equals infinity instead of 1, because infinity is not a set number. Infinity is really such a powerfull statement in any equation, there is not really any way of removing it after it has got there.
If computers could handle infinity programming would be easier for sure. But the thing is that there is not really much you can do with it. If it comes up as the result there is no way of representing it (except with a infinity sign) and if it was part of the equation the result would most likely be infinity.
If you handle infinity as a constant you can still work with it as a multiple, I often consider infinity to be 1 - but beyond our number base. Admittedly this is only ever when i'm thinking about theory, as in practice division by 0 results in a compiler exception.
reminds me of my arguments that points must have a size for the set of points interpretation of lines planes and volmues to make sense
if we somehow try to shoehorn 0 and infinity into the multiplicative group where they clearly dont belong into the only sensible definition would be for 0 to be the inverse of infinity which leads to
0*infinity = 1
although that leaves us with the problem that since cantor realised that there are infinite infities we also have to accept that there would be more than one 0... which one of theseis the neutral in the additive group id rather not think about
Ok, guys, what about this:
you take X=2Y for example.
if you add P/P (=1)
you get
X=P*2Y*1/P
so if P=0, you get 0*2Y*1/0, which would result in an error (1/0 should exist though, but electronics don't want 1/0 to exist (conspiracy? :P), and something times 0 is always 0(although it shouldn't))
but since we just multiplied it in the form of P/P (=1), the outcome SHOULD be the same.
if P=0, then 1/P=infinity
since P/P=1, then 0*infinity should be 1
so I think 0*infinity=1
if that is true, then 0 isn't nothing, but it is a infinite small number (1/infinity)
Nah it ain't.
You just half the distance which doesn't influence the time:
if we pull up this formula: d=0.5^n, then d=/=0
UNLESS we assume that 0 is an infinite small number, then you will be there in an infinite time.
so you end up to be infinitely small mm/nm/pm away from the finish, but you will never get there.
That's an interesting concept, multiple 0's. Although i've several questions and theoretical viewpoints that need challenging.
Firstly, unlike infinities all 0's hold the same value so surely they are all equal to 0, so even if there where multiple 0's all 0's could be expressed as being equal to zero, and therefor be a singular.
Secondly, if zero and infinity are opposites, then does zero need to conform to the same conventions. Does it need to have multiple's, can it not be singular purely because that is the opposite of the infinite plural?
I think 0 is just an infinite small number which is the opposite of the infinite number.
so if there are multiple infinites, there should be multiple 0's as well, seeing 0 should be an infinite small number
and since you can change the infiniteness of the infinite number, you will always have exactly opposite numbers.
Isn't that missunderstanding the concept of 0 though, 0 is a conceptual opposite of infinity, rather than a mathematical opposite which would be expressed as a negative infinity, no?
Everything in mathematics is proven with other mathematical equations.
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