Explain this to me......infinity+1 means that the infinity that you used in the equation wasnt really infinity because you could still have one to add. Explain this to me please.
2007-08-17 13:01:49 · 10 answers · asked by schlynn2000 1 in Science & Mathematics ➔ Mathematics
Its kind of like a man serving a life sentence + 1 day in jail. Its not possible to serve a jail term of 1 day longer than you live. Its more of a concept than an actual number.
2007-08-17 13:10:30 · answer #1 · answered by Triple D 3 · 1⤊ 0⤋
Infinity isn't a number. You can't add anything to infinity.
If you talk about infinity, you're simply saying what happens as some value gets larger without bound.
One example: the limit of (3x^2 + 1) / (x + 1)(x - 1) as x tends to infinity is 3. That just means that as x gets bigger and bigger, the expression gets closer and closer to 3. Give me any difference from three, no matter how tiny, and I'll find you an x big enough that the expression is closer to 3 than that difference. Nowhere do I say that x equals a number called infinity, or that the limit equals 3 times infinity over infinity.
2007-08-17 20:10:25 · answer #2 · answered by Raichu 6 · 0⤊ 0⤋
Infinity doesn't work like a number. Depending on who you ask, adding 1 to it either doesn't make sense, or results in the same thing, infinity (not something larger).
To see why, suppose you have a hotel with an infinite number of rooms; say Room 1, Room 2, Room 3, ..., and so on, infinitely many of them, one for each positive integer.
Suppose the rooms are all full--in some sense, here we have "infinity" guests. But now a new guest arrives. Can you accommodate this guest?
If the hotel had finitely many rooms, the answer would, of course, be no. But with infinitely many rooms, the answer is yes, we can get the new guest a room.
Just tell the person in Room 1 to move to Room 2; tell the person in Room 2 to move to Room 3; and so on. Everyone moves to the next room; since there is no "last room," it is possible for everyone staying in the hotel to do this. This leaves Room 1 vacant for your guest, who moves in. (Since we had "infinity" guests before, now we must have "infinity plus one" guests.)
If you are going to define "infinity plus one" at all, then the only sensible definition is to define it as infinity.
This doesn't mean that infinity is gibberish or silly; it just means that infinity doesn't have the same properties as a number, so we shouldn't treat it like one. We have to be careful when working with infinity.
2007-08-18 14:12:23 · answer #3 · answered by Anonymous · 0⤊ 0⤋
Hey there!
Infinity is not a number. If it was a number, it would follow the basic rules of arithmetic. The following are true about infinity.
infinity+infinity=infinity.
infinity-infinity=indeterminate.
infinity*infinity=infinity.
infinity/infinity=indeterminate.
Infinity is not a number, but a concept. Infinity is used to name a really large number.
Infinity comes a big deal in this problem.
1/0=infinity.
Here's a proof.
1/1=1, 1/0.1=10, 1/0.01=100, 1/0.001=1000 ...
As x approaches closer and closer to 0, of 1/x, then the answer would approach closer and closer to a large number. Instead of saying that the answer diverges, or is undefined, say that the answer is approaching infinity.
Hope it helps!
2007-08-17 22:58:04 · answer #4 · answered by ? 6 · 1⤊ 0⤋
Infinity is not defined as a number. The + is only available for numbers. So there is no infinity + 1.
2007-08-17 20:07:10 · answer #5 · answered by Roy E 4 · 0⤊ 0⤋
Yes, It is strange. Infinity is in a way meaningless because it just can't be plugged into equations like a value. Your question is kind of like this one. How many numbers are in the set of whole even numbers? Infinite right? Okay, now how many numbers are in the set of whole numbers? Twice as many right? Nope just plain old infinite. I guess it's just one of those concepts that is hard for the mind to grasp.
2007-08-17 20:14:23 · answer #6 · answered by gliss 2 · 1⤊ 0⤋
Well, Infinity is not a number (or at least not a normal one), so infinity+1 would not exist.
The symbol infinity represents an infinite amount of 'something' whether it be numbers or hairy little hamsters.
In mathematics it is used in higher level math, such as limits and calculus.
2007-08-17 20:09:22 · answer #7 · answered by AibohphobiA 4 · 0⤊ 1⤋
Consider infinity to be an INDEFINITELY large number. So large that what you divide something by it, you get something INDEFINITELY small, so small that you can't distinguish it from zero. In this case, you can still add one to infinity and still have an infinity as a result...
2007-08-17 20:13:13 · answer #8 · answered by NC 7 · 1⤊ 0⤋
Infinity isn't really an exact number - it's a concept.
Maybe this will help....
2007-08-17 20:08:22 · answer #9 · answered by Eric C 6 · 0⤊ 0⤋
That's exactly the problem. Infinity isn't really a number, its a concept, so you can't just add one to it, because you can never actually reach it.
Infinity is one of the hardest concepts for math students to grasp.
For instance, there is an infinite number of whole numbers. There is an infinite number of fractions. But the number of fractions is greater than the number of whole numbers, even though they are both infinite. It's just too hard to consciously wrap your head around it, so it's best to just try and accept it.
2007-08-17 20:05:56 · answer #10 · answered by Jon G 4 · 2⤊ 2⤋