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

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Discussion Overview

The discussion revolves around the question of whether an equation remains true if both sides are undefined. Participants explore the implications of undefined values and the concept of equality in mathematical statements, particularly in the context of a test scenario involving specific values for x.

Discussion Character

  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant suggests that if both sides of an equation yield undefined results, it could be interpreted as "infinity = infinity," implying the equation is true.
  • Another participant counters that undefinedness or infinity cannot be treated as numbers, thus cannot be equated, challenging the initial assertion.
  • A third participant clarifies that the truth of statements depends on the logical connectors used (e.g., "and" vs. "or") and emphasizes that values themselves cannot be true or false.
  • Further discussion includes the idea that even if infinity is considered within a number set, it does not imply that infinite values can be equated.

Areas of Agreement / Disagreement

Participants express disagreement regarding the interpretation of undefined values and their implications for equality. There is no consensus on whether an equation with undefined sides can be considered true.

Contextual Notes

Participants do not fully explore the definitions of undefined values or the conditions under which equality holds, leaving some assumptions unaddressed.

breebreebran
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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?
 
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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.
 
breebreebran said:
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
breebreebran said:
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.
breebreebran said:
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
 
breebreebran said:
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.
 
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 anyone specific number. An infinite value might be countable, or uncountable, for example, and those would never equal to each other.
 

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