Pure math 2 : 0 = 1!

Number Theory Level 1

Consider the following proof.

0 = ( 1 − 1 ) + ( 1 − 1 ) + ( 1 − 1 ) + … + ( 1 − 1 ) → 1 ⟹ 0 = 1 + ( − 1 + 1 ) + ( − 1 + 1 ) + … + ( − 1 + 1 ) → 2 ⟹ 0 = 1 + 0 + 0 + … + 0 → 3 ⟹ 0 = 1 → 4 0 = (1-1) + (1-1) + (1-1) + \ldots + (1-1) \rightarrow \fbox{1}\\ \implies 0 = 1 + (-1+1) + (-1+1) + \ldots + (-1+1) \rightarrow \fbox{2}\\ \implies 0 = 1 + 0 + 0 + \ldots + 0 \rightarrow \fbox{3} \\ \implies 0 = 1 \rightarrow \fbox{4}

The above is a Mathematical fallacy .

If you know that the proof is wrong, find which step is being wrong .

2 3 4 1

Viki Zeta by Viki Zeta , 19, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Viki Zeta
Jul 3, 2016

The answer is step 2, let’s see why. STEP 1 : 0 = ( 1 − 1 ) + ( 1 − 1 ) + … + ( 1 − 1 ) STEP 2 : 0 = 1 + ( − 1 + 1 ) + ( − 1 + 1 ) + . . . + ( − 1 + 1 ) If you look at the above step, first "1" is being taken out, and "-1", "1" are being pared. So the last 3 pares will be 0 = 1 + . . . + ( − 1 + 1 ) + ( − 1 + 1 ) − 1 Here, "-1" is being left, as first "-1" and next "1" are being pared, last "-1" have no pare to be subtracted with, So the wrong step is 2 \text{The answer is step 2, let's see why.} \\ \text{STEP 1 : } 0 = (1-1) + (1-1) + \ldots + (1-1) \\ \text{STEP 2 : } 0 = 1 + (-1 + 1) + (-1 + 1) + ... + (-1 + 1) \\ \text{If you look at the above step, first "1" is being taken out, and "-1", "1" are being pared. So the last 3 pares will be} \\ 0 = 1 + ... + (-1 + 1) + (-1 + 1) - 1 \\ \text{Here, "-1" is being left, as first "-1" and next "1" are being pared, last "-1" have no pare to be subtracted with, So the wrong step } \\ \text{is} \fbox{2}

3 Helpful 0 Interesting 0 Brilliant 0 Confused

Nice question! Its is obviously obvious tgat should obviously choose option 2 :P

Ashish Menon - 4 years, 11 months ago

If I may, what is a Pare?

Refath Bari - 4 years, 11 months ago

Log in to reply

Sorry typo. I was to mean paired

Viki Zeta - 4 years, 11 months ago

Log in to reply

Ah, I see. It was being repeated quite often, so I thought it was some other-world terminology. Cheers!

Refath Bari - 4 years, 11 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...