How many points are there on the radius?Motor Daddy said:there are TWICE AS MANY points on a diameter as there are on the radius!
Can you show, rather than just insist, that there are twice as many points as this on the diameter?
How many points are there on the radius?Motor Daddy said:there are TWICE AS MANY points on a diameter as there are on the radius!
How many points are there on the radius?
Can you show, rather than just insist, that there are twice as many points as this on the diameter?
What does (1-0.999...) equal?
If no third point exists (can be found) between two points, then the two points cannot be consecutive, they must be the same point in that case.
You're confusing the integers with the reals: there is no integer between two consecutive integers and a finite number between any two distinct integers, the reals have an infinite number of points between any two points which are distinct.
(1 - 0.999... ) = (1.000... - 0.999... ) = 0.000...1 . This value is something non-zero, infinitesimal which is tending towards zero but not equal to zero.
What is your concept of 0.000...1?
How do you pronounce 0.000...1? Like, I pronounce 0.01 as "1 Hundredth." One hundredth to me means that if I divide a line segment of 1 meter in length into 100 parts, .01 meters means exactly 1 of those parts. Exactly one of those parts. Exactly one of those parts!!!
How many parts does the meter long line segment have to be divided into in order for the parts to equal 0.000...1?
'0.000...1' means between the '.'(point) and '1' there are infinity numbers of '0's(zeros).
This is an 'infinitesimal', which has a limiting value towards '0'(zero). Its value is tending towards zero but not equal to zero.
You have to put infinite numbers of '0' before 1 after the point('.'). So, it is similar to dividing the line segment by infinity. You can consider it as 1/(1000...infinity times '0') .
What's 2 x infinity?Motor Daddy said:So the answer to your question is that there are an infinite quantity of infinitely small points on the radius, but there are TWICE AS MANY infinitely small points on the diameter as there are on the radius!!!
What's 2 x infinity?
What you seem to have missed is that you need to count all the (infinite) points to show that the diameter contains twice as many as the radius. Then you will find that the radius and the diameter have an uncountable number of points, so they have the same number of points.
What's 2 x infinity?
What you seem to have missed is that you need to count all the (infinite) points to show that the diameter contains twice as many as the radius. Then you will find that the radius and the diameter have an uncountable number of points, so they have the same number of points.
What's 2 x infinity?
What you seem to have missed is that you need to count all the (infinite) points to show that the diameter contains twice as many as the radius. Then you will find that the radius and the diameter have an uncountable number of points, so they have the same number of points.
What's 2 x infinity?
'0.000...1' means between the '.'(point) and '1' there are infinity numbers of '0's(zeros).
This is an 'infinitesimal', which has a limiting value towards '0'(zero). Its value is tending towards zero but not equal to zero.
You have to put infinite numbers of '0' before 1 after the point('.'). So, it is similar to dividing the line segment by infinity. You can consider it as 1/(1000...infinity times '0') .
But probably a lot stronger than Motor Daddy's.someguy said:Quite a weak mathematical argument. The real numbers and the power set of the real numbers are two uncountable sets, but there is no bijection between them.
So 0.999...+0.000...1=1.0?
So it's really BS that .999...=1 because it's really 0.999...+0.000...1 that equals 1? Will you please speak out of just 1 side of your neck? Thanks.
So adding that to .999... doesn't quite bring the grand total to 1.0?
Is that what you are saying? Are you saying that 0.999...+0.000...1 is tending towards 1 but not equal to 1? Speak more clearly so that I too can understand your intended meaning instead of receiving what I perceive to be a smoke screen. I'm choking...help. (rolls eyes)
So after an infinite amount of 0's there is a one at the end? I take it there are zeros after that 1, or is it not allowed to put another number after the 1 in 0.000...1???
There is no such thing as .000...1. What decimal notation means is that you are assigning a numeral to each of the decimal positions 1, 2, 3, 4, ... So it makes no sense to say there's a "1 at the end" because there is no end. Your notation is not defined.
There are no infinitesimals in the real numbers. What you say makes no sense. Does the value if 3 "tend towards" something else? A number has a value, it doesn't "tend towards" anything.
May be it is right but what i have said is also right.Even in Nonstandard Analysis, where they have a way of making infinitesimals legit, it's still a theorem that .999... = 1.
In my example above this is same as y.It's totally false to say that you can "consider" .000...1 to be any such thing, or anything at all. The notation has no standard definition, and you haven't provided one.
YES.
Adding 0's after 1 in a decimal number does not change its value. If you put another number after 1 other than 0 but keep on adding 0's before 1, this number will still tend towards 0 but not equal to 0.
If you consider the axis of real numbers, it will become a continuous straight line, where all the points correspond to some real number. An infinitesimal is something non-zero. Do you think that the infinitesimal will not correspond to any point in this axis of real numbers?
NO!
What you don't realize is that when you put a "1" in a decimal position it represents a specific quantity. As I explained before, 0.01 means there is a "1" in the "hundredths" decimal position. So in order to place a "1" in a decimal position you have to define which position it is that you are going to position that "1." You have no idea which position it is, and if you did then you would have to eliminate the ... because then there wouldn't be an infinite series of 0's, there would be a FINITE quantity of 0's, then a 1. You then would know which decimal position the "1" was in. But again, you can't do that!
Maybe you don't understand what you are saying when you type 0.000...1. You are saying there are an infinite amount of zeroes after a decimal point, and then at the end of the infinite amount of zeroes there is a one. So the string ends in a 1, which means there is a finite amount of decimal places that the 1 is after the decimal point. That means there is a finite quantity of zeroes before the one. So you are contradicting yourself. On one hand you are saying there are an infinite quantity of zeroes and then a one at the end, and on the other hand you are saying there are a finite quantity of zeroes before a one.
So which is it? Does a one come after a finite quantity of zeroes, or does a one come after an infinite quantity of zeroes? Are the zeroes infinite or finite?
I will explain this in a different way.
Consider the following equations.
1 - 0.9 = 0.1;---(1)
1 - 0.99 = 0.01;---(2)
1 - 0.999 = 0.001;---(3)
1 - 0.9999 = 0.0001;---(4)
1 - 0.99999 = 0.00001;---(5)
.
.
.
1 - 0.9999999999 = 0.0000000001;---(6)
.
.
.
From the above equations we can make a general rule as:" 1 - 0.9...n times 9 = 0.0...(n-1) times 0 then 1; where n is a positive integer greater than 0".---(7)
In the equation (7)
if n = 1, it becomes equation (1);
if n = 2, it becomes equation (2);
if n = 3, it becomes equation (3);
.
.
if n = 10, it becomes equation (6);
Like this it will continue.
In the equation (7) if n becomes infinity, it becomes "1 - 0.999... = 0.000...1" .