Why does 0! = 1 0! = 1? All I know of factorial is that x! x! is equal to the product of all the numbers that come before it. The product of 0 and anything is 0 0, and seems like it would be
.0i = 0 0 i = 0 is a good choice, and maybe the only choice that makes concrete sense, since it follows the convention 0x = 0 0 x = 0. On the other hand, 01 = 0 0 1 = 0 is
Is there a consensus in the mathematical community, or some accepted authority, to determine whether zero should be classified as a natural number? It seems as though formerly $0$ was
Several years ago I was bored and so for amusement I wrote out a proof that 0 0 0 0 does not equal 1 1. I began by assuming that 0 0 0 0 does equal 1 1 and then was eventually able to
.In the set of real numbers, there is no negative zero. However, can you please verify if and why this is so? Is zero inherently quot;neutralquot;?
.But if x = 0 x = 0 then xb x b is zero and so this argument doesnt tell you anything about what you should define x0 x 0 to be. A similar argument should convince you
.Is a constant raised to the power of infinity indeterminate? I am just curious. Say, for instance, is $0^\\infty$ indeterminate? Or is it only 1 raised to the infinity that is?
As for the simplified versions of the above laws, the same can be said for 00 = 0 0 0 = 0, so this cannot be a justification for defining 00 = 1 0 0 = 1. 00 0 0 is ambiguous in the same way that
92 The other comments are correct: 1 0 1 0 is undefined. Similarly, the limit of 1 x 1 x as x x approaches 0 0 is also undefined. However, if you take the limit of 1 x 1 x as x x approaches
.0 0 = x 0 0 = x 0x = 0 0 x = 0 x x can be any value, therefore 0 0 0 0 can be any value, and is indeterminate. 1 0 = x 1 0 = x 0x = 1 0 x = 1 There is no such x x that
Why does 0! = 1 0! = 1? All I know of factorial is that x! x! is equal to the product of all the numbers that come before it. The product of 0 and anything is 0 0, and seems like it would be
.0i = 0 0 i = 0 is a good choice, and maybe the only choice that makes concrete sense, since it follows the convention 0x = 0 0 x = 0. On the other hand, 01 = 0 0 1 = 0 is
Is there a consensus in the mathematical community, or some accepted authority, to determine whether zero should be classified as a natural number? It seems as though formerly $0$ was
Several years ago I was bored and so for amusement I wrote out a proof that 0 0 0 0 does not equal 1 1. I began by assuming that 0 0 0 0 does equal 1 1 and then was eventually able to
.In the set of real numbers, there is no negative zero. However, can you please verify if and why this is so? Is zero inherently quot;neutralquot;?
.But if x = 0 x = 0 then xb x b is zero and so this argument doesnt tell you anything about what you should define x0 x 0 to be. A similar argument should convince you
.Is a constant raised to the power of infinity indeterminate? I am just curious. Say, for instance, is $0^\\infty$ indeterminate? Or is it only 1 raised to the infinity that is?
As for the simplified versions of the above laws, the same can be said for 00 = 0 0 0 = 0, so this cannot be a justification for defining 00 = 1 0 0 = 1. 00 0 0 is ambiguous in the same way that
92 The other comments are correct: 1 0 1 0 is undefined. Similarly, the limit of 1 x 1 x as x x approaches 0 0 is also undefined. However, if you take the limit of 1 x 1 x as x x approaches
.0 0 = x 0 0 = x 0x = 0 0 x = 0 x x can be any value, therefore 0 0 0 0 can be any value, and is indeterminate. 1 0 = x 1 0 = x 0x = 1 0 x = 1 There is no such x x that
Why does 0! = 1 0! = 1? All I know of factorial is that x! x! is equal to the product of all the numbers that come before it. The product of 0 and anything is 0 0, and seems like it would be
.0i = 0 0 i = 0 is a good choice, and maybe the only choice that makes concrete sense, since it follows the convention 0x = 0 0 x = 0. On the other hand, 01 = 0 0 1 = 0 is
Is there a consensus in the mathematical community, or some accepted authority, to determine whether zero should be classified as a natural number? It seems as though formerly $0$ was
Several years ago I was bored and so for amusement I wrote out a proof that 0 0 0 0 does not equal 1 1. I began by assuming that 0 0 0 0 does equal 1 1 and then was eventually able to
.In the set of real numbers, there is no negative zero. However, can you please verify if and why this is so? Is zero inherently quot;neutralquot;?
.But if x = 0 x = 0 then xb x b is zero and so this argument doesnt tell you anything about what you should define x0 x 0 to be. A similar argument should convince you
.Is a constant raised to the power of infinity indeterminate? I am just curious. Say, for instance, is $0^\\infty$ indeterminate? Or is it only 1 raised to the infinity that is?
As for the simplified versions of the above laws, the same can be said for 00 = 0 0 0 = 0, so this cannot be a justification for defining 00 = 1 0 0 = 1. 00 0 0 is ambiguous in the same way that
92 The other comments are correct: 1 0 1 0 is undefined. Similarly, the limit of 1 x 1 x as x x approaches 0 0 is also undefined. However, if you take the limit of 1 x 1 x as x x approaches
.0 0 = x 0 0 = x 0x = 0 0 x = 0 x x can be any value, therefore 0 0 0 0 can be any value, and is indeterminate. 1 0 = x 1 0 = x 0x = 1 0 x = 1 There is no such x x that
Why does 0! = 1 0! = 1? All I know of factorial is that x! x! is equal to the product of all the numbers that come before it. The product of 0 and anything is 0 0, and seems like it would be
.0i = 0 0 i = 0 is a good choice, and maybe the only choice that makes concrete sense, since it follows the convention 0x = 0 0 x = 0. On the other hand, 01 = 0 0 1 = 0 is
Is there a consensus in the mathematical community, or some accepted authority, to determine whether zero should be classified as a natural number? It seems as though formerly $0$ was
Several years ago I was bored and so for amusement I wrote out a proof that 0 0 0 0 does not equal 1 1. I began by assuming that 0 0 0 0 does equal 1 1 and then was eventually able to
.In the set of real numbers, there is no negative zero. However, can you please verify if and why this is so? Is zero inherently quot;neutralquot;?
.But if x = 0 x = 0 then xb x b is zero and so this argument doesnt tell you anything about what you should define x0 x 0 to be. A similar argument should convince you
.Is a constant raised to the power of infinity indeterminate? I am just curious. Say, for instance, is $0^\\infty$ indeterminate? Or is it only 1 raised to the infinity that is?
As for the simplified versions of the above laws, the same can be said for 00 = 0 0 0 = 0, so this cannot be a justification for defining 00 = 1 0 0 = 1. 00 0 0 is ambiguous in the same way that
92 The other comments are correct: 1 0 1 0 is undefined. Similarly, the limit of 1 x 1 x as x x approaches 0 0 is also undefined. However, if you take the limit of 1 x 1 x as x x approaches
.0 0 = x 0 0 = x 0x = 0 0 x = 0 x x can be any value, therefore 0 0 0 0 can be any value, and is indeterminate. 1 0 = x 1 0 = x 0x = 1 0 x = 1 There is no such x x that