Zero is also an integer. If we multiply zero by any number we get zero as answer. Then how we will get product of any two integers is not zero. Could u pls explain.
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ZERO DIVIDED by zero is quite indeterminate. For if A is B times C, then A divided by B is C. But zero is equal to zero times any number whatever. Therefore zero divided by zero is any
MUST ANY number multiplied by zero always equal zero? When only digits are put to paper, it seems so, but when expressed in ordinary language, a different result is possible: if you multiply the total value of the change in your pocket by zero, the original amount remains. Another example of the effect of tangible quantities: taking two circles whose circumferences have been calculated from their identical radii, and dividing the circumference of either into the other will never get you
TO SAY that "any number divided by zero is infinity" is not quite correct. Considering normal arithmetic, it is not possible to divide by zero. This is because "dividing by x" is really just a shorthand way of saying "calculating the amount which gives the original when multiplied by x". Since multiplying by zero always gives zero, we really cannot divide anything non-zero by zero. In fact, remembering that "dividing by ..." is a shorthand for something involving multiplication, even dividing. The "infinity" notation is, in this sense, a convenient shorthand, but not one that is universally valid. In short, if we remember that "division by" and "infinity" are convenient notations that are sometimes, but not always, useful, then it shouldn't be too hard to believe that zero divided by zero really is not definable.
MATHEMATICS is an abstract language which describes the behaviour of the things which we call numbers. The fact that it can be related to the real world is fortuitous and convenient. However it is far from always the case. Pi is a number in any proper sense (as too is e - the number I talk about below). These numbers have an interesting property, amongst others - it is impossible to write them down, unless you accept some error, because they contain an infinite "number" of digits. Hence in any "real" experiment one will always get into the mess which Jack Belck describes (above). On the other hand, 0/0 is undefined, not indeterminate. This might sound pedantic but leads to some important consequences. It can approach a particular value under given conditions and only when those conditions are applied, for example if I take a function such as: f(x)=(1-exp(x))/x then when x=0: f(x=0)=-1, because although when x=0, f(x)=0/0 it approaches this value in an ordered way. Try it out with a piece of graph paper and a pocket calculator, or do the Taylor expansion
The questioner is asking us to follow through the consequences of some hypotheses in a general number system. (They do not apply to any number system of any use, as explained by previous answers.) His second hypothesis gives zero divided by zero equals one and the third gives zero divided by zero equals infinity. From this we can immediately conclude that in any number system satisfying his hypotheses, infinity is equal to one.
If we additionally assume that "zero divided by zero" means "the unique number which gives zero when muliplied by zero", we see that zero is also equal to the common value of one and infinity, and to any other numbers that may exist in the system under consideration.
To sum up: under the conditions given, every number is equal to the same value, call it zero, one, infinity or whatever you like.
Pelham Barton, Birmingham, UK
Must any number multiplied by zero always equal zero?If you multiply the total value of change in your pocket money,the original amount eventually remains.
MUST ANY number multiplied by zero always equal zero? When only digits are put to paper, it seems so, but when expressed in ordinary language, a different result is possible: if you multiply the total value of the change in your pocket by zero, the original amount remains. Another example of the effect of tangible quantities: taking two circles whose circumferences have been calculated from their identical radii, and dividing the circumference of either into the other will never get you
TO SAY that "any number divided by zero is infinity" is not quite correct. Considering normal arithmetic, it is not possible to divide by zero. This is because "dividing by x" is really just a shorthand way of saying "calculating the amount which gives the original when multiplied by x". Since multiplying by zero always gives zero, we really cannot divide anything non-zero by zero. In fact, remembering that "dividing by ..." is a shorthand for something involving multiplication, even dividing. The "infinity" notation is, in this sense, a convenient shorthand, but not one that is universally valid. In short, if we remember that "division by" and "infinity" are convenient notations that are sometimes, but not always, useful, then it shouldn't be too hard to believe that zero divided by zero really is not definable.
MATHEMATICS is an abstract language which describes the behaviour of the things which we call numbers. The fact that it can be related to the real world is fortuitous and convenient. However it is far from always the case. Pi is a number in any proper sense (as too is e - the number I talk about below). These numbers have an interesting property, amongst others - it is impossible to write them down, unless you accept some error, because they contain an infinite "number" of digits. Hence in any "real" experiment one will always get into the mess which Jack Belck describes (above). On the other hand, 0/0 is undefined, not indeterminate. This might sound pedantic but leads to some important consequences. It can approach a particular value under given conditions and only when those conditions are applied, for example if I take a function such as: f(x)=(1-exp(x))/x then when x=0: f(x=0)=-1, because although when x=0, f(x)=0/0 it approaches this value in an ordered way. Try it out with a piece of graph paper and a pocket calculator, or do the Taylor expansion
The questioner is asking us to follow through the consequences of some hypotheses in a general number system. (They do not apply to any number system of any use, as explained by previous answers.) His second hypothesis gives zero divided by zero equals one and the third gives zero divided by zero equals infinity. From this we can immediately conclude that in any number system satisfying his hypotheses, infinity is equal to one.
If we additionally assume that "zero divided by zero" means "the unique number which gives zero when muliplied by zero", we see that zero is also equal to the common value of one and infinity, and to any other numbers that may exist in the system under consideration.
To sum up: under the conditions given, every number is equal to the same value, call it zero, one, infinity or whatever you like.
Pelham Barton, Birmingham, UK
Must any number multiplied by zero always equal zero?If you multiply the total value of change in your pocket money,the original amount eventually remains.
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yes it is right that if we multiply an 0 with a real no. we got zero..
but this is also an exceptional
but this is also an exceptional
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