How to prove the following?

  • Thread starter thescienceboy
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In summary, the statement "there exists X such that for all Y and Z, X+ Y= Z" is false because there is no single value of X that can satisfy the equation for all possible values of Y and Z. This can be proven by choosing specific values for X, Y, and Z that do not result in the equation being true.
  • #1
thescienceboy
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Hey guys,

do you now how to prove that the statement "there exists X such that for all Y and Z X+Y=Z" is FALSE. Seems easy but I can't figure out any counter example to the statement.

Thanks
 
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  • #2
Do you understand WHY it is false? "There exists X such that for all Y and Z, X+ Y= Z" means that we can find a specific X such X+ Y= Z for any Y and Z- in other words, X is chosen FIRST. That is there must exist a specific number X so that X+ Y= Z for any Y and Z.

X+Y= Z is the same as X= Z- Y. Okay, suppose X= -1. Choose Y= 2 and Z= 3. X+ Y= -1+ 2= 1 which is NOT equal to Z= 3. The statement is false for X= -1. Now suppose X is any number other than -1. Let Z= X+1 and Y= X+ 2. Then X+ Y= X+ X+ 2= 2X+ 2. That is equal to Z=X+ 1 only if 2X+2= X+ 1 or X= -1 which is false.
 

1. How do I prove a hypothesis?

In order to prove a hypothesis, you must conduct experiments and collect data that supports your hypothesis. You can also use statistical analysis to determine the significance of your results and further support your hypothesis.

2. What is the scientific method?

The scientific method is a systematic approach used by scientists to conduct experiments and gather evidence in order to answer a question or test a hypothesis. It involves several steps, including making observations, forming a hypothesis, conducting experiments, analyzing data, and drawing conclusions.

3. Can I prove something to be true beyond a reasonable doubt?

No, the scientific method does not allow for absolute proof. Scientists can only support or reject a hypothesis based on the evidence gathered. However, with enough evidence and replication of results, a hypothesis can become widely accepted as a theory.

4. How do I ensure the validity and reliability of my results?

To ensure the validity and reliability of your results, it is important to control all variables in your experiment, use a large and diverse sample size, and replicate your experiment multiple times. You should also use reliable and accurate measurement tools and techniques.

5. Can I prove a theory to be true?

Theories are well-established explanations for a phenomenon that have been extensively tested and supported by evidence. While they cannot be proven to be absolutely true, they are considered to be the most accurate and reliable explanations we have based on current evidence and understanding.

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