• I believe it is zero.
• Well zero times anything is always zero. So i would go with zero
• no it is infinity.
• lim x->0(x*inf) = lim x->0 (inf)= inf
• It's actually not undefined, but it is indeterminate.
• zero times any number is zero. infinity is not a number. truthfully, the multiplication of a 3 dimensional object, or concept by zero, is that object or concept. If you multiply by zero, then the multiplication is zero not the source.
• ZERO!
• It depends. 4-x tends to zero as x tends towards 4. 1/(4-x) tends to infinity as x tends towards 4. Multiply them, you get 1, whatever x is, even if you let it be 4. 8-2x tends to zero as x tends towards 4. 1/(4-x) tends to infinity as x tends towards 4. Multiply these, you get 2, whatever x is, even if you let it be 4. 4-x tends to zero as x tends towards 4. 1/(4-x)^2 tends to infinity as x tends towards 4. Multiply: you get 1/(4-x) which increases without limit as x tends to 4, so surely the answer is infinity. So it depends how the infinity entered the question in the first place. Questions with infinity aren't precise unless you define the infinity. There are hyperfinite numbers greater than any natural number. We might take one of them as our definition of infinity. 0 times a hyperfinite number is definitely zero. EDIT: What's with all the trolling?
• It is undefined because infinity is undefined. So let's define it. Using a trig description: tan (90) degrees. Let's represent 0 as cos (90). Now we know that tan(X)*cos(X) = sin(X) so our tan(90)*cos(90)=sin(90) or 1. In fact this product can be shown to equal any positive number from 0 to infinity except zero or infinity. It is better to leave it undefined because defining it creates a plethora of other undefined objects.
• I believe that zero is defined and infinity is not, therefore zero times anything is still zero.
• It is zero. Think about how multiplication works. You have ten baskets with five apples in each. So you have fifty apples. If you have zero baskets with five apples in each. You have zero apples. No matter how large the number of apples in each basket, if you have zero baskets you have zero apples.
• 1. If, Defintion [ 1 ÷ ( 0 ) = (1∞) = (∞) ] [ 2 ÷ ( 0 ) = { 1 ÷ ( 0 ) } X 2 = (2∞) ] [ 3 ÷ ( 0 ) = { 1 ÷ ( 0 ) } X 3 = (3∞) ] [ 4 ÷ ( 0 ) = { 1 ÷ ( 0 ) } X 4 = (4∞) ] [ 5 ÷ ( 0 ) = { 1 ÷ ( 0 ) } X 5 = (5∞) ] [ 6 ÷ ( 0 ) = { 1 ÷ ( 0 ) } X 6 = (6∞) ] [ 7 ÷ ( 0 ) = { 1 ÷ ( 0 ) } X 7 = (7∞) ] [ 8 ÷ ( 0 ) = { 1 ÷ ( 0 ) } X 8 = (8∞) ] [ 9 ÷ ( 0 ) = { 1 ÷ ( 0 ) } X 9 = (9∞) ] 2. [^^^] = [ 1 ÷ ( 0 ) = (∞) ] = [ 1 / ( 0 ) = (∞) ] = [ 1 / ( 0 ) = (∞) / 1 ] = [ 1 X 1 = ( 0 ) X (∞) ] = [ 1 = ( 0 ) X (∞) ] = [ ( 0 ) X (∞) = 1 ] 3. [^^^ ] = [ ( 0 ) X (∞) = 1 ] = [ ( 0 ) X (∞) = 1 ] = [ ( 1 - 1 ) X ( 1 / 0 ) = 1 ] = [ { ( 1 - 1 ) X 1 } / ( 0 ) = 1 ] = [ { ( 1 - 1 ) } / ( 0 ) = 1 ] = [ { ( 0 ) } / ( 0 ) = 1 ] = [ ( 0 ) / ( 0 ) = 1 ] = [ ( 0 ) = 1 ] 4. Clear contradiction [^^^ ] = [ ( 0 ) X (∞) = 1 ] = [ ( 0 ) X (∞) = ( 0 ) ]
• It is undefined because infinity is not a number, and therefore it is not meaningful to perform mathematical operations on it.
• Zero times infinity is undefined. Think of this in more abstract terms. Picture the limit as x goes to zero of the function (ax)/(x). This function, for any value x, must equal a, because the x terms cancel out. However, at the same time, because x goes to zero, the limit is equal to 0/0. Therefore, in this instance 0/0 = a. Now, we can rewrite 0/0 as (0/1)*(1/0) because 0*1 = 0 and 1*0 = 0. 0/1 = 0 and 1/0 = infinity, therefore 0/0 = 0 * infinity, which in the above instance equals a. Therefore, 0 * infinity has no set value and is thus undefined. While this may seem conterintuitive given the elementary-school definition of multiplication, it is none-the-less correct.
• look up the Cantor Dust Set.
• 6-25-2017 The problem, as usual, is that a lot of people pretend to know something when they don't. Zero is zero: we know that for sure. But there are two definitions for infinity, and neither of them is sure. One defines zero as A NUMBER larger than you can measure. The longest ruler we have is the Earth's orbit, and we can triangulate to get accurate measurements out to about 3200 light years. Beyond that is infinity, but some dingbats claim they can measure longer distances by being excessively clever. The other definition for infinity is "limitless", which is not a practical concept. But that doesn't stop people from making up "gee whiz" factoids about it. Now let's get real: If you take zero steps an infinity of times, how far have you gone?