1 does not equal 1. Care to dispute?
Of course it does
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Actually it doesn't
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I care to dispute. - If I present to you one apple, would you tell me I don't have one? - What you've uncovered is a mathematical inconsistency. The error lies in the fact that you're willing to state that 1x1/3 = .333r, but take issue with 3x.333r = 1. You can't have it both ways to argue your point. A third of 1 is no less .3333r than 1 is .333rx3. Side: Of course it does
Mathematically if you have 1 third of an apple that is the equivalent on paper to .333r, if you have 3 .333r what do you have? Supposedly 1 whole, however you don't when you do the math on paper you have .999r. Physically there is one, mathematically on paper there isn't. Side: Actually it doesn't
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Mathematically, you can't represent 1/3 on paper exactly, if the whole is 1. So your equation didn't represent 1/3 in the beginning, therefore had a chain reaction making your equation wrong. Your equation on paper should look more like this: 1/3+1/3+1/3=3/3 or 1 Side: Of course it does
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My interest lies in both "mathematically" and "on paper". You agree with my apple example which is why you're applying the fraction conundrum to it, so I have already proven 1 = 1. From it's humble beginnings counting fruit and money, math has served us as a means to calculate amounts in our physical world, hence the roots lie in real numbers. When considering more elevated calculations we move farther away from the physical ramifications of the calculations into straight theory such as algebraic formula, quantum mechanics etc.. (which is fine), but the physical implications must remain the goal, as math is little more than a technology to serve man (real). One apple is one apple, and since it can't be argued, I have proven that 1 =1. On to the conundrum. 1/3 of 1 is .333r which would put the amount somewhere in the area between .33r3 and .33r4, which would allow for the total to reach 1. It's repeating forever for a reason. It's accepted in the mathematical field that you can divide 1 by 3 to get .333r but not the other way around, whereas the reality of it is, that .333r is exactly a third of 1. It's the mathematical field that's flawed in this aspect, not the concept. 1/3 of 12 is 4, we don't have a problem here, so the issue lies with the infinity behind .333r that we must view as an entity, not an abstract concept that boggles the mind. Side: Of course it does
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1 cherry pie consist of y cherries. 1 world consist of many factors within itself; # of trees, population, cars, etc. 1 item equals X molecules. Break down of that 1 item can even be farther, protons, neutrons and electrons. 1 is rarely a singular number, but represents a more complexed unit. Thus making 1 not equal to 1, but equal to x, y, x to the c power, etc. Numbers are just a means to describe something and are always subjective to the outcome desired. Side: Actually it doesn't
All your original mathematical statements are correct. However, the conclusion you draw is incorrect. You are essentially equating a world to its inhabitants, or to its environment. We know that none of those are in fact equal. Therefore, you are able to say that one world is equal to one world. Not one world is equal to some other quantity of a different nature. Where 1 is the world and 2 is a human, we cannot say (correctly) that 1=2. Side: Of course it does
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I agree with you that I failed to compare apples with apples in regards to the world example, but the point I was making is the same anyway. Where 1 is rarely a singular number and represents some unit that in reality is more than 1. A better example may have been 1 bushel of apples where the number of actual apples is x. Side: Of course it does
Okay, lets take the classic example of when 1 doesn't equal itself. 1/3 equals what? .333 repeating ( in decimal form ), what is 3 thirds? Your immediate response is most likely 1. However what is .333 times 3? .999 Repeating, so if 3/3 doesn't equal 1, what does? Side: Actually it doesn't
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3*(3.333...) = 9.99999 ... = E (9/[10^n]) from 0 to infinity converges at one. meaning it'll never go past one and continually approach it, if you allow it to run for infinity(sure, not really a practical option) it'll be the same as saying one. think of it as being at n = infinity; E 9/[10^n]) = 1; sure infinity isn't a number but i hope you see what it means. Side: Of course it does
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