x + x = 2x infinity + infinity = 2 infinity (or) infinity x-x=0 infinity * infinity = square of infinity (or) infinity :tongue:
have though alot about zeros and infinities... not a very high level maybe, but hey, I'm just 17....:) about infinity + infinity = 2*infinity ? see it like this.. in a 1cm line, there are infinite many points ... in a 2cm line there is also infinite many points.... so if you have 2 1cm lines they will have infinite+infinite points, which is also infinite as the 2cm line also had infinite many points... hope I wasnt confusing..... and infinity * infinity = square of infinity ? you have a line of any length with infinite many points.. say 1cm again if you have four lines forming a square with, then, the area of 1cm^2 you will have infinite many points in the area...... so the lines of infinite many points, make a square with infinte * infinte many points in the square, which as said earlier his infinite.. so infinity * infinity = infinity.. I have some problem with infinity - infinity though... I have infiinity.... I add another infinity and get.. infinity.. so If i subtract infinity now, I should get ack to my original number or? so x+x-x = x or?? in case of infinty we get x+x-x != x weird.. but however.. its intresting stuf... have some other stuff i have thought of.. will post it another time.......
since infinity is a proper subset of infinity+infinity, they can be put in one-to-one correspondence to eachother, and are then the same "degree" of infinity, am I right?
Head... hurting... None of this makes any sense until you adopt some definitions... and then once you have, it's clear how things work.
Infinity is not a number, it is a mathematical concept. The reason it isn't a number is because for ever number at 'infinity' there is always a number that is greater than it. It doesn't make very much sense to use the concept of infinity as a mathematical operator. Limits are the best way to show this correlation. If something is unbounded then it is useless to try to find a maximum number for Infinity.
x=.9999999............... 10x=9.999999............. 10x-x=9x=9.000000000000 x=1 thus 1=.99999999.............. 1/3=.33333...... 3(1/3)=3(.333333...........) 1=.999999999999999........
also how about this one: construct a right triangle, say a triangle with sides=1 and with hypotenuse sqrt(2). obviously sqrt(2)>1, how then can all the points on the side that has length of sqrt(2) be matched to all the points on the line that has length 1 like shown in the picture? this problem mystified Leibniz
I believe he tried to illustrate that a line twice as long can be projected down on the first line as if two sides of a triangle, and you can match up each point on one line to each one on the other... therefore, they must have equal number of points?
sorry to ruin your fun but your example doesnt work.. :tongue: 2x=x is ONLY true for 0 and infinity... so when you have 2x=x and divide by x to get 2=1, you actually divide by 0 or infinity. And as divison by 0 and infinity is undefined your conclusion is invalid...:) just rememebered a quote by J.Baylock.... "If you want somone to hate you, explain to them, logically and politely, why they are wrong" a funny thing of division of 0's can be demonstrated in this way (thought it myself, but someone else may have done it) 0*0=0 divide by 0 at both sides and you get 0=0/0 so is 0/0 equal to 0??? :grumpy: nonono :tongue: 1*0=0 divide by 0 at both sides and you get 1=0/0 hihi :rofl: 2*0=0 divide by 0 at both sides and you get 2=0/0 hihi :rofl: 3*0=0 divide by 0 at both sides and you get 3=0/0 hihi :rofl: can cnotinue as long as I want... (or maybe not til infinity..)
I prefer to think of it like this: ax=x => a=1 or x=0 or x=infinity. so 2x=x => a=2 => x=0 or x=infinity.
You are using operations like multiplication and addition which are only defined on a set of numbers.