Why is 1 not equal to 0 in this proof?

[fresh_42]

(And somebody said it’s proving 1=0 by assuming 1=0. I didn’t get that.)

$25\dfrac{m}{s}$ is a quantity of $25$ meter per second. It says what happens within the timespan of one second, namely a change in location of $25$ meter. It normalizes time. One second becomes the unit, i.e. $1$ second = $1$.

By writing $\dfrac{x}{x-1}$ you introduced the unit $x-1$ which thus is treated like $1$ wheras it still equals $x-1=1-1=0.$ In this sense, you treated $1$ as $0$. You made $1$ second $0$ seconds.

 

[DrClaude]

This is a new predicate that we can get from the previous one by squaring both sides

You mean multiplying by $x$ on both side.

 

[DrJohn]

This divide by 0 was a joke / trick we used to play on the younger kids at school when I was a teenager. And that was a long time ago! We used to set them up with the basics and say look, this proves 1 = 0 and watch as they approached the maths teacher for help.

Why are we still discussing this in a TWO page thread?! Dividing by zero is just not allowed. End of.

And remind yourself of when it was posted here...

 

[DrJohn]

PS people my age may remember that The Who released a single in 1971 called "wont get ****** again"

 

[fresh_42]

This divide by 0 was a joke / trick we used to play on the younger kids at school when I was a teenager. And that was a long time ago! We used to set them up with the basics and say look, this proves 1 = 0 and watch as they approached the maths teacher for help.

Why are we still discussing this in a TWO page thread?! Dividing by zero is just not allowed. End of.

And remind yourself of when it was posted here...

No. This is exactly why math in school does not work. Instead of providing any insights, it's simply forbidden. This is not how education works, at least not on PF. Why is it forbidden? You only offer: "because it is". Truth is, the why question can be answered on many levels, and we did not even touch all of them!

Shut up and calculate might work in quantum physics, but it does not work in mathematics. Not even at school, as can be seen at any school of your choice.

 

[PeroK]

No. This is exactly why math in school does not work. Instead of providing any insights, it's simply forbidden.

When I was at school I could see for myself that division by zero was problematic. I don't see any deficiency in my reasoning in those days that required advanced abstract mathematics. I certainly wasn't guilty of "shut up and calculate". Quite the opposite!

 

[fresh_42]

Since this thread has obviously turned into a general mocking about why we discuss it at all, I will close it by now. The original question has been answered on many levels anyway.