0.99999999999999... is not the same as 1. It is off by 0.00000000000000...1. End of discussion.
| a.l.e.x59 said: 0.99999999999999... is not the same as 1. It is off by 0.00000000000000...1. End of discussion. |
This comment allong with your avatar made me laugh.
BTW, try putting down this answer on a math test and see what the teach gives you.
JHawkNH said:
That is incorrect. The irational numbers are a different number set then the rational numbers. By definition because of this you can not find an irrational number between to rational numbers. |
The rational numbers are a countably infinite set which when combined with the irrational numbers forms the real numbers ...
| txags911 said: False. 0.9999~ is not an irrational number any more than 0.333~ is. It is 3 * 0.3333~ (or 3 * 1/3) (or 1) An infinitely repeating number is not necessarily an irrational one. That's the mistake you made. Incidentally, the true proof is that between any two non-equal REAL numbers, there is an infinite number or other real numbers between them. So if 0.999~ and 1 are not the same, you should be able to name at least 1 number between them. |
You're correct in that not all repeating numbers are irrational, but 0.999... is an irrational number
You can not express it as a ratio of two other numbers thus it is irrational.
Anyways ... I'm taking my math degree in pure mathematics and leaving this thread ...
JHawkNH said:
This comment allong with your avatar made me laugh. BTW, try putting down this answer on a math test and see what the teach gives you. |
LOL: I totally made the connection with my post, and Eggman's anger. Made it seem as if I was a mad scientist of perfection or something. Every time I post something with extreme logic, or anger, I can't help but visualise it coming from Eggman, especially when I look at my avatar. Yeah, I'll put my answer down on my next math test, if the question calls for it.
Yes, they are both equal, anyone who thinks otherwise is advised to pay a little more attention in math class from now on.
If they weren't the same number, then you would be able to choose a third number between them (this is true of any 2 unique numers.)
So I ask, what number is between .99999 repeating and 1?
I don't understand! The number 1 behind the infinite number of 0s still exists. There is a number 1 (a number that makes a difference) hidden within the infinite amount of 0s, that is the difference between 0.999... and 1. Clearly, 0.999 is not 1. Sure, you might be able to make it equal 1 by an awkward mathematical equation. I didn't really even understand that mathematical equation anyways. All I know if that it is less than 1.
No alex, it is not, you said so yourself, you don't understand infinite numbers.
Because .9999... repeats infinitely, the 1 in 0.0000....1 never actually exists, because those 0's go on forever. You CAN'T put a number at the end of a .... those dots imply an infinite series or 0's.
| HappySqurriel said: 0.999... is an irrational number You can not express it as a ratio of two other numbers thus it is irrational. |
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| Kytiara said: I'm pretty sure it doesn't work that way txags911. edit: I guess I should extrapolate a little. Take x to equal 0.9999 x = 0.9999 You can then continue adding 9's towards infinity and it never changes. What you are implying is as x nears infinity, the number tends towards 1 which is true, however it never reaches 1, just gets really really close. |
You forgot that it isn't 9.9999, it's 9.9999.... so your equation means nothing
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