"I'm not back." - Bill Harding, Twister
Originally posted by James Christian:
Hence I define Zero as being the mere abcense of something in a defined subsystem.
"Thanks to Indian media who has over the period of time swiped out intellectual taste from mass Indian population." - Chetan Parekh
There are only two hard things in computer science: cache invalidation, naming things, and off-by-one errors
Originally posted by Jim Yingst:
[James]: there is no smallest number greater than 0 and hence no greatest number lesser than 1.
Out of curiosity, when was the last time anyone here argued otherwise? Who?
Something that is infinite cannot equal something that is finite like an integer or float number.
Originally posted by James Christian:
And finally what about this? 7.1000(0)1 Is this the smallest number greater than 7.1?
The soul is dyed the color of its thoughts. Think only on those things that are in line with your principles and can bear the light of day. The content of your character is your choice. Day by day, what you do is who you become. Your integrity is your destiny - it is the light that guides your way. - Heraclitus
Originally posted by fred rosenberger:
James,
can you define for me what you mean by "0.000(0)1"??? What most people seem to think is that the (0) means "an infinite number of 0s". but then you say "put a 1 after that".
The soul is dyed the color of its thoughts. Think only on those things that are in line with your principles and can bear the light of day. The content of your character is your choice. Day by day, what you do is who you become. Your integrity is your destiny - it is the light that guides your way. - Heraclitus
Or we can listen to them to get a better understanding what they mean. Until then, I'll be asleep in the corner.
I've heard it takes forever to grow a woman from the ground
"I'm not back." - Bill Harding, Twister
Originally posted by James Christian:
Especially for you Mr. Singh:
Shall we throw errors for 1 + 0?
What about 7 - 0?
"Thanks to Indian media who has over the period of time swiped out intellectual taste from mass Indian population." - Chetan Parekh
Originally posted by R K Singh:
If you have $1000 in the bank and you take the $1000 out how much will be left in the bank?
Originally posted by Adrian Wallace:
$1000 - $998.75 = $0
"Thanks to Indian media who has over the period of time swiped out intellectual taste from mass Indian population." - Chetan Parekh
There are only two hard things in computer science: cache invalidation, naming things, and off-by-one errors
code:
void orangesPerEmployee(int oranges, int employees){
return oranges/employees;
}
if orangesPerEmployees = 0, code will likely assume:
"Oh, there weren't any oranges for the employees! We must need more oranges"
when in fact there was 6.022 x 10^23 oranges, just no employees.
code:
x^2 - 3x -10
y = ----------------
x - 5
Originally posted by fred rosenberger:
James,
This might not be the BEST example, but it is an example where dividing by 0 giving a value does not work...
I'm going to write a program that takes an equation and graphs it, like many calculators will do. If I use your definition, when i graph something like
i would get a nice, neat, solid line equivilent to y = x+2. The program would never think anything was wrong.
But mathematically, my graph should have a hole in it at x=5. there is no y value at that point. With the exception being thrown, my program will say "AHA!!! something is wrong here. Don't graph a point at x=5 because it doesn't exist".
Piscis Babelis est parvus, flavus, et hiridicus, et est probabiliter insolitissima raritas in toto mundo.
Originally posted by Steven Bell:
It seems to be you could use a similar argument to remove the NullPointerException from Java. Any code that would currently throw a null pointer exception should simply do nothing and if a return value is expected simply return null.
I'm tired of checking for null's all the time anyway.
Piscis Babelis est parvus, flavus, et hiridicus, et est probabiliter insolitissima raritas in toto mundo.
There are only two hard things in computer science: cache invalidation, naming things, and off-by-one errors
There are only two hard things in computer science: cache invalidation, naming things, and off-by-one errors
Piscis Babelis est parvus, flavus, et hiridicus, et est probabiliter insolitissima raritas in toto mundo.
Piscis Babelis est parvus, flavus, et hiridicus, et est probabiliter insolitissima raritas in toto mundo.
Originally posted by Joel McNary:
I've got the TI-86 (Which is simply the newer version of the TI-85). When I trace the graph, I can get it to read x=5 y=7 at the bottom, and I don't seem to have a hole in my graph.
There are only two hard things in computer science: cache invalidation, naming things, and off-by-one errors
Seeing as you explained that the equation that looks complicated is in actual fact a simple linear graph does it seem normal to you for a linear graph to have a hole in it?
Where would you place the hole in y = x + 2 or 2y = x ?
And this hole which you defined as being exactly a point in size. How big is a point in mm? Would it not be our infamous smallest number greater than 0 which we have already agreed does not exist? Would you not agree that your calculators are producing a flawed graph by inserting a hole in a linear graph?
I'm no mathematical expert but I never remember my teacher saying that linear graphs have a hole in them. Wouldn't you find it strange and inconsistent that a calculator produces a graph without a hole when given y = x + 2, yet produces a graph with a hole from a more complex input which mathematically simplifies to the same thing.
Your forgetting that when i transform an equation, I can't change the Domain. the domain of the original equation said "x can be anything but 5". so, after the transformation, I MUST STILL USE THE SAME DOMAIN.
if the input was y = x + 2, then no, i would not expect a hole. but that was NOT my input.
Find a high school Algebra II textbook (maybe Algebra I). I'm not an expert either, but i distinctly remember teaching this very concept to my students when i taught high school.
All things considered, wouldn't my proposed implementation of division by 0 give a more consistent output?
no. if you allow division by 0, all mathematics breaks down. allowing it lets me prove that 1=2, 1=3, 1=4. your idea that 5/0 = 5 allows for me to also say with just as much validity that 5/0 = 11. Plus, before division could be done by the hardware, it would have to check to see if the denom is 0. if it were, it would have to use one rule, and if not, use another.
And furthermore seeing as before it was argued that since multiplication and division are inverse operations shouldn't they cancel one another out?
just as 2*5/2 cancels to produce 5 where is the problem with cancelling
for all values of x even when x happens to equal 0?
because, by the very definition of division, you CANNOT divide by 0. you can cancel the (x-5)s in ALL CASES EXCEPT WHEN x = 5. in that case, you can't cancel it out, so your stuck with the original equation. which gives you a 0 in the denominator. which is, by definition, undefined. there IS no solution at that point.
There are only two hard things in computer science: cache invalidation, naming things, and off-by-one errors
Originally posted by James Christian:
With regard to our 0.111(1), 0.333(3) etc. I wanted to add a final comment.
The reason we propose with this notation to append an infinte number 3's to 0.333 is because no matter how many 3's we append the actual amount is always slightly greater, and the second we append a 4 the actual amount is always slightly less. Therefore when we say that 1/3 = 0.333(3) what we are actually saying is that due to an inadequacy of expression in base 10 we denote 1/3 as 0.333(3) because no matter how many 3's we append the actual amount is always slightly greater. So we hypothesize that 1/3 is equal to 0.333 with an infinite number of 3's appended. However, as has already been agreed since infinity is a number which does not exist we cannot say that 1/3 is EXACTLY equal to 0.333 with an infinite number of 3's appended as such a number cannot and does not exist.
Hence when we say that 0.333(3) (which is merely an imperfect representation of 1/3) * 3 = 0.999(9) what we are actually saying is that the result is always slightly greater than 0.999 no matter how many 9's we append. However, contrary to 1/3 we have no difficulty in exactly representing this number in base 10 as it is precisely equal to 1.
Piscis Babelis est parvus, flavus, et hiridicus, et est probabiliter insolitissima raritas in toto mundo.
"I'm not back." - Bill Harding, Twister
it simply has no size - as in it has a width of 0, and a height of 0
i did not say "it is in fact a simple linear graph". what i said was, using algebra, we can convert the 'complicated' equation into a 'simpler' one, with the same solution set (i.e. for every x in the the domain, i get the same y in the range). However, since my original equation does NOT allow for me to have an x value of 5, i can't use an x value of 5 in my 'simplified' version of the equation. it's simply not allowed.
now, if i were JUST graphing y = x+2, then there would be no hole. but i am not. i am graphing that more complicated equation. So i am bound by ITS domain. HOW i go about graphing that is irrelavent to the actual solution.
erroneous use of the term "hypothesize".
"I'm not back." - Bill Harding, Twister
Right, so what your so saying is, is that your graph has a hole with width and height equal to 0.
Errrm, isn't that the same as there being no hole?
Do both graphs produce the same line?
There are only two hard things in computer science: cache invalidation, naming things, and off-by-one errors
There are only two hard things in computer science: cache invalidation, naming things, and off-by-one errors
"I'm not back." - Bill Harding, Twister
You can have a capacitance that has 0 voltage and 0 charge, sure.
There are only two hard things in computer science: cache invalidation, naming things, and off-by-one errors
thanks. I really don't know physics or electronics very well. i just went to a physics web page and grabbed a formula that would (IMHO) help substantiate my point.