Any reason for this paradox?

It's an indeterminate form. In summary, there is an explanation for why these seemingly contradictory equations appear. In the first case, dividing by zero leads to an invalid result. In the second case, canceling out a zero term also leads to an invalid result.
  • #1
PhysicoRaj
Gold Member
538
49
I'm sure there must be some explanation to why these kind of things appear..

firstly,
consider a=b
ab=b2
a2-ab=a2-b2
a(a-b)=(a+b)(a-b)
a=a+b
since a=b,
b=b+b
1=2 !??


then this one-
(100-100)/(100-100)
=[(10+10)(10-10)/10(10-10)]
=2

Anything has gone wrong?
 
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  • #2
PhysicoRaj said:
I'm sure there must be some explanation to why these kind of things appear..

firstly,
consider a=b
ab=b2
a2-ab=a2-b2
a(a-b)=(a+b)(a-b)
a=a+b
Since a = b, then a - b = 0. To get to the line above, you divided by zero, which is never allowed.
PhysicoRaj said:
since a=b,
b=b+b
1=2 !??


then this one-
(100-100)/(100-100)
=[(10+10)(10-10)/10(10-10)]
=2

Anything has gone wrong?
Here you canceled (10 - 10)/(10 - 10), which is 0/0. You can't do that.
 
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1. What is a paradox?

A paradox is a statement or situation that seems to contradict itself, yet may still be true.

2. What are some examples of paradoxes?

Some examples of paradoxes include the grandfather paradox, where a person travels back in time and prevents their own birth, and the liar paradox, where a statement claims itself to be false.

3. Why do paradoxes occur?

Paradoxes often occur when our assumptions or expectations about a situation are challenged or when there is a logical inconsistency in our thinking.

4. How do scientists deal with paradoxes?

Scientists often try to resolve paradoxes by examining the underlying assumptions or by expanding our knowledge and understanding of the subject. They may also use mathematical models or experimental evidence to help explain the paradox.

5. Can paradoxes be beneficial in science?

Yes, paradoxes can be beneficial in science as they can lead to new discoveries and insights. They can also challenge existing theories and lead to the development of new ones.

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