2010-03-11, 06:35 PM
(This post was last modified: 2010-03-11, 06:37 PM by Horusmaster.)
ClawofBeta Wrote:They have some faulty premises.
"For any two different real numbers, you can pick a third number which is between them."
Who said that?
*facepalms that's the definition of real number
If the difference between two numbers is zero, then they are equal. For example, 5 - 5 = 0 because 5 = 5.
The difference between 1.0000... and 0.9999... is:
1.0000... - 0.9999... = 0.0000...
= 0
Therefore, they are equal.
Their arguement is bs. Sure, "..." might mean going on forever, but 1.0000... - 0.9999... = 0.0000(keep on going) until 1. This applies to the 3rd problem, too.
there won't be a "1" at a bottom, because the number goes on forever, forever means no end. If there is a 1, then the numbers does not go on forever, if you keep your reasoning, you'll fail calculus when you learn it
"0.9999... gets closer and closer to 1, but never reaches it."
Closer and closer? How can it be getting closer and closer? It's one number! Try the limit argument, above.
"0.9999... is a decimal representation of infinity, not a number."
Well, how come it's DEFINITELY bigger than 0.5 and smaller than 2? Just because something has infinitely many pieces doesn't mean it's infinite. Zeno figured this out 2500 years ago.
I disagree with the first quote, as it is one number, but... and with the second one, Xeno is just a crazy mathematician who's problems no one can really solve. One of them is like this:
Take the distance between you and an object. Cut it by half. Theoretically, you can keep on cutting in half into infinite. But....wouldn't this mean we can't be able to walk to that object, since it's infinite? So the universe is all screwed up and we're all gonna die.
There is obviously a flaw in his reasoning because he's only doing the limit up to the time that you and the object intersects, but not past it, that have nothing with this.
The rest of his arguements are logical, but I still disagree due to my trig. teacher saying 0.999... approaches 1, but never gets there, and she had this entire complicated proof and crap.May I tell you that high school teachers are not mathematicians?
ShiKage Wrote:1 is an integer. 0.9999999 repeated isn't. Therefore 1 != 0.9999999999999. 0.9999999999999 is a number which is missing a fragment of its ability of becoming a whole number. Whether that be impossible to see the difference in, it's still not the same as the integer "1." It's still not a whole number.
so 0.5+0.5 is also not a integer, "one" is not a integer because it must be "1".