Why might he not have considered 0-n?
202541
Think about the number bar... if you start at 'n' and then move 0 distance from it toward the left, you are still at 'n'.\n\nFor 0-n, you would start at 0, and move 'n' distance toward the left, so 0-n = -n ... the only case where 0-n=n, is when n=0.
278593
In line 5, you are dividing by x-y. Since x = y, then x - y equals zero.\n\nYou can not divide by zero.
128411
Anything divided by 0 is actually undefined, not infinity or 0. When you think about how that works, it makes sense:\n\nDividing a numerator by smaller numbers makes your number larger. Divide 4 by 2, you get 2. Divide 4 by 1, you get 4. Divide 4 by 0.5, you get 8. And so on until you are dividing by a number so small it's pretty close to 0. The overall number gets larger and goes off into infinity.\n\nBut, if you divide a negative number in the same manner, your number gets smaller. -4 by 2 is -2, -4 by 1 is -4, -4 by 0.5 is -8, etc. As you approach 0, your numbers go off into negative infinity.\n\nYou'll have the same weird effect if you divide by negative numbers - a positive divided by an increasingly smaller negative will yield negative infinity, and a negative divided by an increasingly smaller negative will yield positive infinity.\n\nYou can't have it both ways - dividing by zero yields both a positive and negative infinity! So someone a long time ago decided that since a number can't really have two values, it will be undefined.
44404
That's untrue.  Quite in fact, the absence of the zero stifled the advancement of mathematics in the west for a long time.  Zero is a number of fundamental importance.\n\nI don't know where you're getting your info.  Perhaps someone got an award from some group of idiots that thought he was being clever, but zero is far, far, far, far, far from being nonsense.\n\nSomeone is jerking your chain, bro.  Give up onit already.  You need to recognize that you were duped and move on.
73309
You know that he probably didn't mean this in a quantitative sense.  Twice might have meant relative to temperature from the day before, or relative to the mean temperature for this time of year, ...\n\n\nQuantitatively, the term "twice as cold" needs to be relative to some baseline, the fact that it is 0 degrees currently is immaterial: 0 degF = -18degC = 255 degK, so you can't just multiply the value by '2' or you will get different values (the same value, a colder temperature, and a much higher temperature, respectively).
45913
The answer would not be no.
456495
Do not write x = 0 because think about it\n\nif x = 0, then that would mean that |0+4| + 4 = 0\n\nthat means 8 = 0... is that true? NO!\n\nSince it is imposible for |x - 4| to equal -4 (since absolute value is ALWAYS possitive or 0) there is no solution =)
187451
Because (no+1) is like adding +1 and -1, in other words the sum is zero.  When you cancel out the (no+1) from both sides in line 4, you are dividing by zero, which gives rise to all kinds of contradictions and paradoxes in mathematical proofs, even proofs like this one.
507116
No, because the opposite of -5 is 5 which is positive; the opposite of 0 is 0 which is neither positive nor negative.\n\nThis is why the expression "-x" should never be read as "negative x" but rather "the opposite of x" since if x itself were negative, -x would be positive.
372363
It is not possble!\n\nConsider the Fibonacci sequence 0, 1, 1, 2, 3, 5, 8 ..... This is clearly unbounded as |Un| > |Un-1|\n\n1, x, 1 + x, 1 + 2x, 2 + 3x. 3 + 5x, 5 + 8x ......\n\nIf x = 0 this is the Fibonacci sequence starting at U1 and so is still unbounded\n\nThe general term of the above sequence is therefore Un+1 + x* Un (Un, Un+1 of the Fibonacci sequence)\nNow Un diverges and so xUn also diverges\nIf x > 0, the divergence is more rapid\nif x < 0 the sequence oscillates without bound\n\nNB 1, 0, 1, 0, 1, 0, 1, ... does not follow the rules set \n\nshould go 1, 0, 1, 1. 2, 3, 5, ......
220479
0 as a number\n\n0 is the integer that precedes the positive 1, and follows −1. Zero first appeared as a number in Brahmagupta's work dated to 628. Prior to that Babylonians used a space marker that played one of the functions of zero. Babylonians did not have a special symbol for zero. In most (if not all) numerical systems, 0 was identified before the idea of 'negative integers' was accepted.\n\nZero is an integer which quantifies a count or an amount of null size; that is, if the number of your brothers is zero, that means the same thing as having no brothers, and if something has a weight of zero, it has no weight. If the difference between the number of pieces in two piles is zero, it means the two piles have an equal number of pieces. Before counting starts, the result can be assumed to be zero; that is the number of items counted before you count the first item and counting the first item brings the result to one. And if there are no items to be counted, zero remains the final result.\n\nWhile mathematicians all accept zero as a number, some others would say that zero is not a number, arguing one cannot have zero of something. Others hold that if you have zero dollars in your bank account, you have a specific quantity of money in your account, namely none. It is that latter view which is accepted by mathematicians and most others.\n\nAlmost all historians omit the year zero from the proleptic Gregorian and Julian calendars, but astronomers include it in these same calendars. However, the phrase Year Zero may be used to describe any event considered so significant that it virtually starts a new time reckoning.\n\n\n\n0 as a numeral\n\nThe modern numeral 0 is normally written as a circle or (rounded) rectangle.\n\nOn the seven-segment displays of calculators, watches, etc., 0 is usually written with six line segments, though on some historical calculator models it was written with four line segments. This variant glyph has not caught on.\n\nEarly Europeans hesitated to consider zero as a numeral or number. Leonardo of Pisa or Fibonacci says the following in 1202 AD when the Indian number system arrived in Europe.\n\n"After my father's appointment by his homeland as state official in the customs house of Bugia for the Pisan merchants who thronged to it, he took charge; and in view of its future usefulness and convenience, had me in my boyhood come to him and there wanted me to devote myself to and be instructed in the study of calculation for some days. \nThere, following my introduction, as a consequence of marvelous instruction in the art, to the nine digits of the Hindus, the knowledge of the art very much appealed to me before all others, and for it I realized that all its aspects were studied in Egypt, Syria, Greece, Sicily, and Provence, with their varying methods; and at these places thereafter, while on business.\n\nI pursued my study in depth and learned the give-and-take of disputation. But all this even, and the algorism, as well as the art of Pythagoras, I considered as almost a mistake in respect to the method of the Hindus. (Modus Indorum). Therefore, embracing more stringently that method of the Hindus, and taking stricter pains in its study, while adding certain things from my own understanding and inserting also certain things from the niceties of Euclid's geometric art. I have striven to compose this book in its entirety as understandably as I could, dividing it into fifteen chapters.\n\nAlmost everything which I have introduced I have displayed with exact proof, in order that those further seeking this knowledge, with its pre-eminent method, might be instructed, and further, in order that the Latin people might not be discovered to be without it, as they have been up to now. If I have perchance omitted anything more or less proper or necessary, I beg indulgence, since there is no one who is blameless and utterly provident in all things."\n\nLeonardo of Pisa \nHere Leonardo
312427
The answer is 1 - you're raising a quantity to a power of 0, which always results in 1. The quantity within the parentheses contains no division by zero, so I know it's a real number, too.
410967
There's got to be additional information to the problem...\n\n(-1,-4) is simply a coordinate point on a plane.  \n-1=x coordinate\n-4=y coordinate\n\nhowever, if the problem is a proof then the statement is false because 9(-1)+3(-4)= -21 ...not 8
174505
haha, but this does not work. you cannot mathematically divide by (a-b) because this quantity is equal to 0. (1-1)=0. Dividing by zero yields an indeterminate answer.
66911
The construction of negative numbers and rational numbers is much more complex than you think. So 3 over -1 is not an arithmetic operation and using the rules of abstract mathematics it can easily be seen it is true.
74001
in the second step, you completely cahnge the equation...b/c you started out w/ -1=-1, however, in the 2nd step you divided -1/1 and 1/-1, those AREN'T equal\n\nand also the obvious reason that 1 DOES NOT= -1
210639
Zeno ignored the fact that the infinitely many smaller steps take infinitely less amounts of time to do.\n\nAs the earlier answerer pointed out, sum the power series and you get a finite value for the time taken...\n\nLike a lot of these logical tricks, there's something being forgotten or ignored to make it look impossible.