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pretty much all non-repeating decimals. I say this because I do not agree that they are EXACTLY the same (.999 repeating and 1; .333 repeating and 1/3). Lets just say that if they were lines/curves then .333repeating approaches but never touches 1/3. Once again, I say that they might as well be the same, but aren't. The fact that it isn't exactly the same is pretty much negligible.
but 1/3 = 0.1 in base 3, which is non repeating. Or, 1/2 = 0.111repeating in base 3 (but 0.5 in base 10). Seems like whether a number is rational or not shouldn't depend on what base you're working in.
They did make theory of relativity practically false When they discovered that black holes past the event horizon have more mass (and thus gravity) than legitamately possible via einsteins theory. Also time in the event horizon is roughly half of "regular" time thus time isnt really relative but space is.
No. That's what you are doing.
1/3 as a decimal is way more than a concept... Quite simply:
The theory of relativity is intact. I'm pretty sure Hawking has a lot of information for you on black holes. You seem to have been led astray there. No such discovery is even possible; that or you have misspoken.
I have those on my DVR, so good. Also have the morgan freeman's "into the universe" Havent watched it yet though.
The thing is, Einstein proved Newtons theories wrong about gravity, but in order to calculate the strength of it, Newtons gravity equations still work. Now Einstein and modern black hole and string theory are slightly different, but a similar concept exists. Einsteins theory holds for as far into the universe as is relevant to us. The only exception to Einsteins rule that scientists have theorized are the first 200 something atomic seconds after the big bang, during which time the universe was expanding faster than the speed of light. No other place has any sort of (believable/viable/probable/not insane/most importantly provable) theory suggesteingan object surpassing the speed of light. As far as what you are saying, a guy above me said it. We do not know anything beyond the existance of an event horizon. We can't, because we cant see past it, or even see it, and obviously have not visited it. Even black holes have only been observed indirectly (lack of light). This means that wormholes, new dimensions, and areas which break modern laws of physics are all theories made, albeit by brilliant people, but just to entertain ideas as to the importance of finding a way past the event horizon. Also our universe was made, and the laws of physics formed with it (im religious, but don't believe in the genesis creation), so any argument about the beggining of the universe when even the laws were still non existant, and any alternate dimensions or universes are not valid proof that any theory of physics is false, in the universe at least.
I read through the wiki article, and didn't find anything indicating that these two are not one and the same. You are right in that algebraic proofs are not entirely sufficient, insofar as that if one has trouble understanding .9repeating = 1, they will have some disagreements with the arithmetic involved in those algebraic proofs.Gotta read the whole thing, parts in there show reasoning why it isnt the same but is treated like it is. Algebraic proofs have holes in them and this is just one according to that article.
and whoops i meant steven hawkings but i forgot they came on back to back with Morgan freeman
I ****ing love your avatar
Just out of curiosity, are you speaking of what i mentioned in my first post at the bottom? If not, im curious what you are talking about because i listened to a lecture on real numbers and there derivations and such.
Yeah im just curious what you are talking about
I think this one's been mentioned. At the very least, it's given in the Wikipedia entry that MarsFool posted.
Numbers can be expressed as an infinite sum. There's a way to construct them to do so.
