See below.
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“The Post That (for no discernible reason whatsoever) Uses The Word “Dipthong” Correctly In A Sentence”?
Not that there’s anything wrong with that…
Sorry. Infinity is presently not available. Error 404
So would Infinity be expressed as a negative vector in this equation?
If Infinity could be expressed as a vector, that would imply that Infinity has a direction, and that all other directions do not lead to Infinity.
Infinity is everywhere, and nowhere.
What’s the square root of infinity? On second thought, forget I asked.
The square root of infinity is, of course, infinity.
It’s just a bit smaller version.
So how far do I keep going?
The barber shop I went to as a kid had full length mirrors on the front and back walls, and sitting in my little boost bench (which put me a good four feet from the floor), I would look into the mirror above the waiting customers and see rank after rank of barber shops receding into the distance, until they were too small to be seen; my first exposure to the infinite.
The barber always pretended to snip off my ear with the scissors, showing me his thumb tucked between his index and middle fingers, saying that it was my earlobe. Real card, my barber.
This is even worse than when I got stuck in the “wet hair, rinse, repeat” cycle once. Luckily, I ran out of shampoo after a day or two.
Drat. And, I had things to do today.
Infinity has no square root. It only has a circle root.
Or is it a circle route?
That would be a Great Circle Route, especially if the universe is spherical.
My calculator won’t let me divide by Infinity.
It will, however, let me divide by Lexus.
To infinity and beyond!
I could imagine infinity so much easier as a teenager.
Now, I am a geezer.
I fall upon life’s thorns! I bleed!
Exquisite.
I think the Conceptual Series are my favourites.
But your age is so much closer to it now!
The “obligatory contrarian” reply (Based on the protein wisdom conceptual series)
Keeeep going.
See above.
Depends on what you mean by “smaller”. First, every positive real number maps over into square-root space, so there’s just as “many” square roots of numbers as there are numbers. Second, every real number has two square roots, so for any set N, the square root of N is a set that has twice as many members. Third, negative reals map to complex numbers, which is a whole ‘nother kind of infinity. So, I contend, tongue fully in cheek, that the square root of infinity is actually bigger than infinity.
Sorry, that was me.
That bothered me at first, until I remembered that the product of two negative numbers is a positive number.
But that means negative numbers have no square root.
So, they’re not real. So, the negative set of square roots isn’t real either.
Or am I missing something.
Too complex to explain. In the case of the square root of -1, i is i.
But, literally, the set of square roots of negative numbers isn’t Real, it’s Imaginary.
Complex numbers are numbers that have Real and Imaginary components. If you wonder <i>what the hell for?</i), consider that most of frequency response methods and a great deal of solutions to the differential equations of oscillating systems rests on complex number theory.
Point to the shortest route around the universe, and you’re always pointing at the back of your own head.
[Yet another shameless theft from RAH]
Very good argument. I tried to be clever, but you were cleverer.
I might have a way out.
Are we talking about infinity as an amount, or as a maximum? I was thinking maximum value. I can see that in square-root space you could argue that there are more numbers in square-root space. However, the square-root function “squashes” values significantly. 25 maps to 5, 36 maps to 6, and so on.
Therefore, regular space infinity is larger in a maximum value sense than square-root space infinity, though square-root space infinity holds more values.
The above is completely tongue-in-cheek, of course. I’m not that crazy. I think.
That’s a stretch. Try comparing the number of nonzero digits in 3 with the number of nonzero digits in sqrt(3), sometime.
JFTR, I am no longer even partially serious about this.
I didn’t say number of digits, I said value. Size of the number. 25 is greater than 5. 36 is greater than 6. The square-root function decreases the value of a number, so the space the square-root function maps to is smaller in the sense that the maximum value in the set is smaller. If I take any number and map it to square-root space, the value it maps to is less than it’s original value.
You seem to be talking about cardinality of the set, not the maximum value in the set.
Eh, either way it’s the same of course. Except for countable infinity. I never got that proof.
“countable infinity” sounds oxymoronish to me.
As for cardinality, etc this was intended as more of a Mathemagicianesque treatment of the subject than anything halfway serious.
Just to finish beating this long dead horse in a thread only two people bother reading any more:
The rational numbers (integers and fractions involving integers only) are countably infinite. There’s a proof for this… I didn’t come close to getting it. The reals are “more infinite” in that they are not countable, as they are a superset which wholly contains the rational numbers.
Very weird, I know. When I hit stuff like that my brain failed me. I thought I knew math until then. Got out of the class before my pending “F” could be assigned and got a few other classes substituted for this stuff and graduated without learning it.
Ah. I can see that there’s a difference between the infinity of real numbers and that of integers; rational numbers seems to be in-between-ish.
My math training is directed at applications, which means I missed pretty much everything having to do with, well, infinity.
That’s not math, it’s philosophy. But then, doctorates in math are PhDs too…
I always thought that my collection of Star Wars cards would maintain it’s primary listing on my geek resume.
I think it still holds, but after77 reading these complete comments it’s pretty damn close.
I respectfully disagree. The proof is consistent within the strictures of the system.
Whether the result is useful or not is not the point. Math is a theoretical construct that often has uses in the real world.
It5’s the philosophy of math. There’s nothing that says philosophy can’t be consistent within the strictures of a system—indeed, that’s why the highest degree awarded by universities is the Ph.D.
Everywhere and nowhere, Baby.
Get it right.
Philosophy is the love of wisdom. Maths is a cross between a language and a philosophy.
On of the tragedies of my life is my innumeracy.
And illiteracy of course.
Stick an e on the end there.
The base case reply to prevent overrun (based loosely on the protein wisdom conceptual series and good programming principles)
Okay, if you made it this far, stop.
Okay, I’ll stop.
I’m already infinitely bored with this thread anyway.
Still: my infinity is bigger than yours.
Sez you!
I’m your biggest fan nobody love you like i do