Originally posted by !~TONY~!I thought that was a clever thing you invented. Is ''!='' actually a convention for ''not equal''?
Yeah....notice the awesome Computer Science not equal to also.....I mean, how simple is 2-2 = 0, but 1- .9999... != 0. I mean, I cannot think of much simpler! WHOOOO!
Back in the day, I tried to do mathsy posts on RHP with symbols made of text, but it was way too much work.
Originally posted by royalchickenOh yeah, that is real stuff. Such as:
I thought that was a clever thing you invented. Is ''!='' actually a convention for ''not equal''?
Back in the day, I tried to do mathsy posts on RHP with symbols made of text, but it was way too much work.
if(boolTonyIsSweet != true)
{
cout<<"That is a lie!";
}
Check it out. I am sweet.....That is some C++ though, and I haven't rocked that out in a while, so that may be wrong, but you get the idea. != is a real thing!
Originally posted by !~TONY~!Ok, if you haven't read the topic as a whole then here is your proof (nothing new for the ones who read the entire topic):
I am still a little boggled by this whole discussion. Chicken said .9999... = 1, so I will agree, but I need this explained to me. I see it as.....if you asked yourself if two #'s are the same, their diff. is zero, so
2 - 2 = 0, but 1-.9999.. != 0, so I dunno really. Someone please refute this!
1-0.999... is clearly something (zero or something else). Let's assume the difference is a real number.
Now, what properties does the difference have?
I'm sure you'll agree that;
- It's not negative
- It's smaller then any positive number
I claim that there is only one number with those two properties, namely the number zero (0).
If there's a second real number with those properties, let's call that number N, then we can compare it to 0. With this comparison we have three possibilities;
1) N < 0. Look at what this says, it says that N is negative. That is in contradiction with the first property of N. So it can't be this possibility.
2) N > 0. Look at the number N/2, it is positive and 0 < N/2 < N. But the second property of N states that N is smaller then all positive numbers! Another contradiction, so this possibility isn't the case either.
3) N = 0. With the other two possibilities ruled out, this is the only possibility left.
My claim that there is only one number with the two properties stated was true then. The difference 1 - 0.999... has those two properties, and thus the diference is zero.
exactly, which is why it does equal one
for any finite number of 9's it would be less than one, but with an infinite number of 9's, it differs from 1 by 1/infinity ie 0.
it seems no matter how many times and in how many ways it is demonstrated that 1 = 0.9999rec this thread just restarts with someone saying they still don't believe it. Admitedly it's a quirk of the decimal system which is unaesthethic, but in sandard mathematics, with the least upper bound axiom, it is stilll undoubtedly true.
Why don't you do the subtraction 1.000....rec - 0.9999....rec, and when you find out where the answer differs from 0.000...rec please repost telling us in which decimal place the deviation occurs, then I will grovellingly apologise.
Originally posted by SiskinBetter yet, why not have tlai1992 multiply 39826139816493847 by (1 - 0.9 rec) for us?
exactly, which is why it does equal one
for any finite number of 9's it would be less than one, but with an infinite number of 9's, it differs from 1 by 1/infinity ie 0.
it seems no matter how many times and in how many ways it is demonstrated that 1 = 0.9999rec this thread just restarts with someone saying they still don't believe it. Admitedly it's a ...[text shortened]... post telling us in which decimal place the deviation occurs, then I will grovellingly apologise.
Originally posted by SiskinI think the problem is that those who say 1 > 0.999... either haven't heard of/don't understand the lub axiom or don't like it or any of its equivalents. What people seem to have in their heads is the 'unique decimal expansion axiom', one which immediately fails unless you have infinite natural numbers, never mind real numbers. This would have some rather important consequences, including rendering the reals countable and destroying the standard well-ordering of the naturals.
exactly, which is why it does equal one
for any finite number of 9's it would be less than one, but with an infinite number of 9's, it differs from 1 by 1/infinity ie 0.
it seems no matter how many times and in how many ways it is demonstrated that 1 = 0.9999rec this thread just restarts with someone saying they still don't believe it. Admitedly it's a ...[text shortened]... post telling us in which decimal place the deviation occurs, then I will grovellingly apologise.
I find it pretty amusing that this is a topic debated endlessly on forums that otherwise wouldn't touch maths with a barge-pole. It's becoming an internet tradition! 🙄
Originally posted by AcolyteAye, I'm looking forward to my analysis course, because I don't understand this kind of thing in any great depth (ie I had to look up all the relevant axioms when you gave the ''complete ordered field puzzle). However, I think maths courses should be given better names. For example, ''Analysis 1'' should be ''Basic Lubbing and Glubbing''.
I think the problem is that those who say 1 > 0.999... either haven't heard of/don't understand the lub axiom or don't like it or any of its equivalents. What people seem to have in their heads is the 'unique decimal expansion axiom', one which immediately fails unless you have infinite natural numbers, never mind real numbers. This would have some ra ...[text shortened]... hat otherwise wouldn't touch maths with a barge-pole. It's becoming an internet tradition! 🙄
heh, i can't rhyme the statement 'numbers are infinite' with the statement 'no matter how many 9's there are'
When dealing with infinity you are not discussing "how many" anymore.
Yes, any finite number of 9 gives a non-zero difference. But an infinite series of 9's doesn't...
All as long we're discussing reals! I'm not venturing into the hazardous environments of non-standard spaces :p