Does 0.9999... = 1?

Alexander Hamilton said:
Does 0.9999... = 1?
I have an equation that proves that it does!
Click to expand...

You would indeed need a formula or something to make them equal. Obviously, they are not perceived as equal, and appear to be two different values, not equal ones. Form a pure logical/philosophical point of view, you have already failed. One equals one. Is the value you presented "equivalent" because of your formula? You have no argument from me on that, but the two are not "equal", else you wouldn't need a formula.

The argument has always centered on our perception of "equal" and what that actually means. The fact is, when you divide one into three parts, a remainder exists. This can be demonstrated by dividing a dollar or 10 pennies, One of the three parts will contain a remainder, there is no way around that. Now, does this mean we can't formulate mathematical equations to rectify an insignificant infinite remainder? Not at all! And by doing so, we can utilize base 10 math, and make all kinds of calculations work out! I have never argued this isn't so, or not possible, and yes dumo... 1/3 does exist. It's a fractional representation of value, in this case, a division problem. And in the case of one divided by three, it is a division problem which never finds resolution, as there is an infinite remainder. What three equal percentages should I add to get 100%... that's all I want to know?
 
Dixie said:
You would indeed need a formula or something to make them equal. Obviously, they are not perceived as equal, and appear to be two different values, not equal ones. Form a pure logical/philosophical point of view, you have already failed. One equals one. Is the value you presented "equivalent" because of your formula? You have no argument from me on that, but the two are not "equal", else you wouldn't need a formula.

The argument has always centered on our perception of "equal" and what that actually means. The fact is, when you divide one into three parts, a remainder exists. This can be demonstrated by dividing a dollar or 10 pennies, One of the three parts will contain a remainder, there is no way around that. Now, does this mean we can't formulate mathematical equations to rectify an insignificant infinite remainder? Not at all! And by doing so, we can utilize base 10 math, and make all kinds of calculations work out! I have never argued this isn't so, or not possible, and yes dumo... 1/3 does exist. It's a fractional representation of value, in this case, a division problem. And in the case of one divided by three, it is a division problem which never finds resolution, as there is an infinite remainder. What three equal percentages should I add to get 100%... that's all I want to know?
Click to expand...

successful-troll-is-successful.jpg
 
Dixie said:
You would indeed need a formula or something to make them equal. Obviously, they are not perceived as equal, and appear to be two different values, not equal ones. Form a pure logical/philosophical point of view, you have already failed. One equals one. Is the value you presented "equivalent" because of your formula? You have no argument from me on that, but the two are not "equal", else you wouldn't need a formula.
Click to expand...

Do you not know what an equals sign means? If the two sides of the equation aren't equal, it's not a formula. The entire point of a formula is to prove that two things are equal.
 
Dixie said:
The argument has always centered on our perception of "equal" and what that actually means. The fact is, when you divide one into three parts, a remainder exists. This can be demonstrated by dividing a dollar or 10 pennies, One of the three parts will contain a remainder, there is no way around that. Now, does this mean we can't formulate mathematical equations to rectify an insignificant infinite remainder? Not at all! And by doing so, we can utilize base 10 math, and make all kinds of calculations work out! I have never argued this isn't so, or not possible, and yes dumo... 1/3 does exist. It's a fractional representation of value, in this case, a division problem. And in the case of one divided by three, it is a division problem which never finds resolution, as there is an infinite remainder. What three equal percentages should I add to get 100%... that's all I want to know?
Click to expand...

It depends on whether or not your working with real or hyperreal numbers. If you are working with hyperreal numbers, you can indeed just say "33.333...", and mathematically assume that the 3 goes on forever, which is perfectly valid in this formal system. If you are not using hyperreal numbers, that's not valid, of course.

In the case of 0.999..., you have to borrow some tricks from calculus to sum infiinite series, but once you do so, the result is 1. So 0.999... is = 1 on the hyperreal number line. If you are constrained and unable to use hyperreal numbers, you could only use summations that more and more closely approximate 1 depending on the level of steps you used, but you'd never get to 1 of course, because summing to infinity isn't valid in this context.
 
You must log in or register to reply here.
Back
Top