Question on Infinite

Qfwfq · 01-19-2008

Quote:

Originally Posted by P3X491

is there any difference between infinite +1 and infinite -1?

Well "obviously" the difference is 2... except there's a bit of subtlety behind it. If you mean:

$\lim_{x\rightarrow\infty}((x+1)-(x-1))$

Then the answer is 2 but if you mean:

$(A+1)-(B-1)$

with A and B being two arbitrary infinite terms, then it's an indeterminate form, it only has an answer for some choices of the two terms. Subtle question: Suppose instead of the above example we consider:

$\lim_{x\rightarrow\infty}(x+1)-\lim_{x\rightarrow\infty}(x-1)$

can we still say the answer is 2?

murad_math · 01-20-2008

hmmm, could you please give some more explanations, or a clear context of the word,,,

Pyrotex · 01-21-2008

Well, that's the problem, don't you see? "Infinite" simply means, without end or without boundary. In mathematics, infinity has a special place. For one, it is NOT a number.

That's right, infinity is NOT a number. It is not a member of the integers. It is not a member of the real numbers (like 32.569). It does not follow the same rules of addition, subtraction, multiplication, division that integers and reals do.

You cannot just mix infinity and integers like (Infinity + 1). It really does not make mathematical sense. The concept of "one more than infinity" is senseless.

You have to deal with it the way Qfwfq does above by replacing infinity with "x" and then taking the limit as x approaches infinity. That makes sense. However, if you are not familiar with the elementary concepts of beginning calculus, then it may not make sense to you.

So, get a good book on the introduction to calculus.

freeztar · 01-21-2008

Quote:

Originally Posted by Pyrotex

You cannot just mix infinity and integers like (Infinity + 1). It really does not make mathematical sense. The concept of "one more than infinity" is senseless.

You have to deal with it the way Qfwfq does above by replacing infinity with "x" and then taking the limit as x approaches infinity. That makes sense. However, if you are not familiar with the elementary concepts of beginning calculus, then it may not make sense to you.

So, get a good book on the introduction to calculus.

The above is a perfect explanation for why men cannot model women.

When my lover tells me she "loves me so much", I do the completely irrational retort of "I love you more". This usually goes through three of four evolving iterations until I pull out the "...infinity times 10 to the 23rd power divided by zero!". This usually ends the "competition" with rolling eyes and a slight recognition that her fiancee is a complete dork.

Nonetheless (irrationality aside), as Pyro demonstrated, infinity doesn't mean anything if you can slap a "+1" to the right of it.

Qfwfq · 01-22-2008

Quote:

Originally Posted by Pyrotex

You cannot just mix infinity and integers like (Infinity + 1). It really does not make mathematical sense. The concept of "one more than infinity" is senseless.

Of course you can!

$\infty+1=\infty$

Infinity is not a real number (though hyperreal numbers have been formalized). In the ordinary calculus of real numbers a term can be infinite (in a given limit) and these infinities may be manipulated. A separate although related concept is infinity in the sense of set cardinality ( $\aleph_0$ etc.). There are many pitfalls to watch out for.

Pyrotex · 01-22-2008

Quote:

Originally Posted by Qfwfq

Of course you can!

$infty+1=infty$ ...

That's right, Qf.
Make me wrong!

Show me up!

Hurt my widdle feelings!

I just can't take it any more!

I'm gonna divide infinity by zero so many times (an infinite number of times in no time at all) that it will break your calculator way over there in Italy.