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Hi there, I'm thinking of getting a tattoo (i know, i know), and I want mathematical symbols on my body.
I would like the "There exists" symbol (backwards E) and "Infinity" (the lemniscate), spelling out "There exists infinity".
Does that make sense? What order should I have the symbols? Lemniscate+E or E+Lemniscate?
Thanks, sorry this sounds so weird!
Since you'll be explaining this to everybody who asks, perhaps you could reserve your back for an explanation (either that or your cheeks, so that you could moon anybody who asked, but that would be irreverant).
I would go with E+Lemniscate. However, since the premise is dubious, as there are infinitely more numbers than infinity, perhaps you should leave room for a few more symbols.
"There exists infinity" seems... somehow unsatisfying from a real analysis perspective. Maybe you could say "there exists a unique infinity"? [backwards E, exclamation point, infinity symbol]. Then again, infinity is largely an abstraction and not a mathematical object. The real numbers don't include infinity. When taking limits as something goes to infinity, you're really just making a statement about large-case-trends and not something that a sequence actually does at "infinity". It's just convenient to think of infinity as an object with intuitive properties, though formally it doesn't explicitly appear much as an object. So, saying "there exists infinity" is probably a bit of a misnomer except in rare circumstances.
But, all of this math talk is mostly irrelevant :). The people who'll see the tattoo probably won't have a clue what it'll mean, so what would some random person think of such a tattoo? If you like the answer to that question, go with whatever set of symbols make you happy :thumb:.
The statement is a paradox. Infinity is a concept, used to visualise a number that has no limit. Even if we attempt to consider infinity as a number, we quickly realise that we cannot pin it down, since for any number we can imagine, a larger one exists without end. For infinity to exist, in the real sense, it must have a unique value, which is not compatible with the concept of infinity.
I don't quite think it's a paradox, but yeah infinity certainly isn't a real number. But, it can be a mathematical object in a few cases, such as the extended real numbers. But again that sort of technicality doesn't matter much, since I'd think very few people who will see the tattoo would be into mathematical technicalities.
Mutually exclusive concepts then.
How about:
"1/0 Exists!"
Or use a divisor sign instead of a forward slash. Let the reader do some math. ;)
1/0 does not exist though, at least not in any system I am aware off... (I believe there was some professor trying to allow division by zero by calling it 'nullity' or something but I don't think he knew what he was talking about lol...)
Anyway, 1/0 is not infinity.
In a sense 1/0 exists, in that sometimes people mean lim as x->0+ of 1/0 = inf. But yeah, usually not.
I suppose you could define division by zero to give an object that's not in the regular real numbers, though I don't know what would work well. You probably couldn't have field properties that way at least, which is sorta the point of the reals.
LOL! Of course 1/0 is undefined. So what we have is a tattoo that will generate discussion. Take a look at one of my favorite proofs:Quote:
Originally Posted by NickThissen
X = 1
X^2 = 1
X^2 - 1 = 0
factoring:
(X - 1)(X + 1) = 0
divide both sides of the equation by (X - 1) yields:
X + 1 = 0
But we know that X = 1, so:
1 + 1 = 0
simplify:
2 = 0
Math can be a riot! :D
Since x = 1, (x-1) = 0 and you are dividing by zero --> False proof. (But I bet you knew that :p)Quote:
Originally Posted by Code Doc
Another one:
1 = sqrt(1)
1 = -1 * -1
1 = sqrt(1) = sqrt(-1 * -1) = sqrt(-1) * sqrt(-1) = i * i = -1.
"1 = sqrt(1) = sqrt(-1 * -1) = sqrt(-1) * sqrt(-1) = i * i = -1" was on a homework assignment I was grading yesterday. Talk about coincidental.