If both sides of an equation are undefined does that mean its true?

  • #1
I was taking a test and basically for the answer I had limited it to two choices.
A: x=3 and x does not equal 2
or
B. x=3 x=2

When I plug in three, I got 3/1=12/4 so three is true.
But when I plugged in two I got 3/0=8/0
So would this be true too? Or does x not equal 2?
Wouldnt undefined on both sides be the same as infinity=infinity making it true?
I already turned my test in and I chose B. Was I right?
 

Answers and Replies

  • #2
arildno
Science Advisor
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"Wouldnt undefined on both sides be the same as infinity=infinity making it true?"
Totally wrong. Undefinedness, or infinity for that matter, is not a number, and hence, cannot "Equal" anything, since "equality" is a relation between numbers.

"I already turned my test in and I chose B. Was I right?"
No.
 
  • #3
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I was taking a test and basically for the answer I had limited it to two choices.
A: x=3 and x does not equal 2
or
B. x=3 x=2
Statement A is true if x is equal to 3, and false for all other values of x. If x = 3, the first part is obviously true, as is the second part, since x is not equal to 2.

Statement B - I can't tell, since there is no connector between the two statements. If the missing connector is "and", then the statement is false, since x can't simultaneously be 2 and 3. If the connector is "or", then statement B is true if the value of x is either 2 or 3. It would be false for any other values of x
When I plug in three, I got 3/1=12/4 so three is true.
No, 3 is neither true no false - it's a value. Only statements (such as equations or inequalities) can be true or false.
But when I plugged in two I got 3/0=8/0
So would this be true too? Or does x not equal 2?
Wouldnt undefined on both sides be the same as infinity=infinity making it true?
I already turned my test in and I chose B. Was I right?
No
 
  • #4
mathman
Science Advisor
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I was taking a test and basically for the answer I had limited it to two choices.
A: x=3 and x does not equal 2
or
B. x=3 x=2

When I plug in three, I got 3/1=12/4 so three is true.
But when I plugged in two I got 3/0=8/0
So would this be true too? Or does x not equal 2?
Wouldnt undefined on both sides be the same as infinity=infinity making it true?
I already turned my test in and I chose B. Was I right?
It would help if you displayed the equation you are talking about.
 
  • #5
433
120
Even if infinity exists within a number set, it still can't be counted on to equal itself. Infinity is more like a class of numbers then any one specific number. An infinite value might be countable, or uncountable, for example, and those would never equal to each other.
 

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