Thread: very puzzled

So I was reading this in a book and just couldn't grasp this...

It said:
NOTE
There is no real number x such that
0 (multiplied by) x =1 , so 0 has no multiplicative inverse.

But I thought 0 multiplied by anything was always 0 so how could this be
no matter what x could be the answer would always be be 0 not 1 right?

Is it because x isn't a real number? But still that just doesn't seem right.
please help

Originally Posted by etherealreaper

But I thought 0 multiplied by anything was always 0 so how could this be
no matter what x could be the answer would always be be 0 not 1 right?

You seem to think you are contradicting the book, but what you say supports what the book says.

0x = 1 has no solution in the reals because no matter what you choose for x, there is no way to make 0x equal anything other than 0.

So, there is no value you can multiply 0 by to get 1, hence by definition 0 has no multiplicative inverse.

Philosophic question...

Is definition of "number" such as x=1/0 can contribute in someway to mathematics?

(I studied it a bitter, and I came up with the answer "no")

Originally Posted by Also sprach Zarathustra

Philosophic question...

Is definition of "number" such as x=1/0 can contribute in someway to mathematics?

(I studied it a bitter, and I came up with the answer "no")

Real projective line - Wikipedia, the free encyclopedia

Nice! Thank you!