According to DIY Network

[charlie b]

You can have a nearly infinite number of points in time, and they will still not add up to any duration of time.

It's worse than that, actually. You can have an uncountably infinite number of points in time that don't add up to any duration.

True. But we don't need to go there. The total number of times a voltage or current has crossed the value of zero, starting with the creation of the first AC circuit and continuing up to this day, is very large, but it is finite.

I had hoped to avoid the "countable" versus "uncountable" infinity topic. I hadn't heard it discussed in many years. I still recall losing an argument with my HS math teacher, when he proved to me that the number of points in a 1 inch line segment is the same as the number of points in a 2 inch line segment. He also proved to me that the number of "real numbers" is greater than then number of "integers" (yes there is a higher value of infinity than infinity). The first is "countable," and the second is not.

 

[charlie b]

Can't we agree that it is actually 49.9999999999999999999% of the time positive

I would only agree if you let the 9's repeat to infinity.

 

[al hildenbrand]

. . . (yes there is a higher value of infinity than infinity). The first is "countable," and the second is not.

I recall this described as "strength" of infinity. Infinities can have different strengths.

 

[dlhoule]

charlie

I would only agree if you let the 9's repeat to infinity.

I'll agree to that if you tell me how many 9's it takes to get me to infinity.

 

[charlie b]

At least one more than the ones you have written so far. Try writing a few more, and then ask me if it's enough. :lol: :lol:

 

[dlhoule]

charlie
LOL :lol: :lol: but I haven't done anymore than copy most of them.

 

[ceknight]

. . . (yes there is a higher value of infinity than infinity). The first is "countable," and the second is not.

I recall this described as "strength" of infinity. Infinities can have different strengths.

That's one way of thinking about it, but it's a bit misleading. They're all weaklings.

It really comes down to basic cardinality. An infinite set is considered countable if its members can be put in 1-to-1 correspondence with the set of counting numbers. They use the counting numbers because even though the set of counting numbers is infinite, we can still count them... In mathematical terms, a countably-infinite set has a cardinality of Aleph 0.

Consider, though, that between any two counting numbers there are infinitely many real numbers. In fact, between any two real numbers there's always another one. So the set of real numbers is just gobs and gobs bigger than the set of counting numbers, and try as you might you'll never get them into a 1-to-1 correspondence. That makes the set of real numbers uncountable, with a cardinality of Aleph 1.

The part that really blows peoples' minds is that you can have sets with an even higher cardinality than that, just by performing axiomatic functions like power set on infinite sets. But I'll stop there, because this is waaaayyyy off topic.

 

[charlie b]

That is the very same discussion I recall from High School days. I can even remember how to prove that the set of real numbers is not countable. But I never did know how to spell "Aleph." :wink: :lol:

 

[dlhoule]

"Aleph." Never mind the spelling can any of you math geniuses tell me what the He** it means?

See this is one of the times I wish I had been properly educated.

 

[ceknight]

That is the very same discussion I recall from High School days. I can even remember how to prove that the set of real numbers is not countable. :lol:

Yeah, I forgot to mention in my earlier response that the issue of cardinality is why you lost that bet with your HS math teacher. The set of all real numbers in a 1" line segment has the same cardinality as the set of real numbers in a 2" line segment.

Larry, the Aleph used as a symbol by mathmaticians is the first letter in the Phoenician and Hebrew alphabets.

 

[Mike03a3]

Re: According to DIY Network

Referring to house wiring...

The black wire is positive, the white wire is negative, and the green wire is ground.

Well, they're half right, half the time.

 

[celtic]

Re: According to DIY Network

Referring to house wiring...

The black wire is positive, the white wire is negative, and the green wire is ground.

Well, they're half right, half the time.

Is that like a quarter of the time?

 

[Jim W in Tampa]

At least one more than the ones you have written so far. Try writing a few more, and then ask me if it's enough. :lol: :lol:

49.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999%
OK NOW

 

[charlie b]

Close enough for government work. But then, 12% would also have been close enough for government work. :lol: :lol:

 

[BarryO]

"Aleph." Never mind the spelling can any of you math geniuses tell me what the He** it means?

It refers to "transfinite numbers", an esoteric part of number theory that usually only gets discussed in late night (very late night) bull sessions in the dorm hallway, when talk turns to The Infinite.

This thread goes on a bit longer, and someone will invent calculus on it.

 

[charlie b]

"Aleph." Never mind the spelling can any of you math geniuses tell me what the He** it means?

See this is one of the times I wish I had been properly educated.

It's not a matter of education. Very few people other than professional mathematicians (yes, such things do exist) would ever care about it.

Suppose you knew no foreign languages, and went to Paris. Suppose a waiter placed on your table a spoon and then another spoon, then he placed a fork, another fork, and another fork. You would not need to know what was meant by "deux" and "trois" to recognize that the number of spoons is different than the number of forks. Just treat "Aleph 0" and "Aleph 1" as being words in a foreign language that convey different numbers, and you can walk away not caring to know anything more on the topic.

The tricky part is getting your mind around the possibility that the number of things in one infinite set might not be the same as the number of things in another infinite set. My HS math teacher had to sell me hard on that one, before I bought it.

 

[dlhoule]

Thanks Charlie

Now if I understand things correctly we can have an infinite number of sets each with an infinite number of numbers with each set having a different number of numbers. I had a high school math teacher that gave out seven A's in the class. I got a B. I had the highest test score averages and missed one question on a home work assignment, because I did it using my method which he said wouldn't work all of the time. Well, he spent a week trying to find a case where my way wouldn't work. Lesson well learned. Don't argue with authority unless you have chance of winning argument.
How you can know so much about so many things is amazing!
You have a Great weekend. Be nice to the lady for Mother's Day, though.

 

[Minuteman]

Re: According to DIY Network

Referring to house wiring...

The black wire is positive, the white wire is negative, and the green wire is ground.

I love this place, for here I can find a plethora of information - on and off the topic. In this tread in particular, I have been both entertained and enlightened.

Now... my turn.

Nether the black or white wire are positive nor negative at ANY time.

Better stated, the electrons flowing on the outside of one conductor will read an alternating potential difference relative to the other conductor. However the "wire" has no charge in and of itself.

 

[charlie b]

Be nice to the lady for Mother's Day, though.

Hey, I've already given her her Mother's Day present: the set of lawn furniture she wanted. Actually, what I did was answer the phone when she called from the hardware store, at which time she gave me the aisle number and location, and told me the SKU number on the box. And who ever said it was hard to shop for a gift for your wife? :lol: :lol: I think she might have actually just bought it for herself, except the box was far too big for her car. :shock: