Where Can I Find a Proof That e is a Transcendental Number?

  • Thread starter sutupidmath
  • Start date
  • Tags
    Proof
In summary, "proof" in science refers to evidence or data that supports a hypothesis or theory, obtained through the scientific method. It is never considered absolute, but with strong and consistent evidence, it can lead to widely accepted theories. Evidence is any information that supports or refutes a claim, while proof is based on objective, empirical data. Scientists ensure the validity of their proof through methods such as repeated experiments, peer review, and controlling for variables, as well as considering alternative explanations and collaborating with other researchers.
  • #1
sutupidmath
1,630
4
Can anyone tell me where i could find the proof that e is not an algebracic number, but instead it is transcendent?

thnx
 
Physics news on Phys.org
  • #2
[itex]e^a[/itex] is transcendental for any non-zero algebraic [itex]a[/itex]. This is a consequence of the Lindemann-Weierstrass Theorem, look that up anywhere.
 
  • #3

FAQ: Where Can I Find a Proof That e is a Transcendental Number?

What is "proof" in the context of science?

"Proof" in science refers to evidence or data that supports a hypothesis or theory. It is the result of rigorous experimentation and analysis, and is used to make conclusions about the natural world.

How do scientists go about finding proof?

Scientists use the scientific method to find proof. This involves making observations, forming a hypothesis, designing and conducting experiments, analyzing data, and drawing conclusions based on the evidence. It is a systematic and objective approach to understanding the world around us.

Can proof ever be considered absolute?

No, proof in science is never considered absolute. Scientific knowledge is always open to revision and can change based on new evidence. However, with a strong and consistent body of evidence, a theory can be widely accepted and considered well-supported.

What is the difference between "proof" and "evidence"?

Evidence refers to any information or data that supports or refutes a claim, while proof is a specific type of evidence that is strong enough to support a hypothesis or theory. Evidence can be subjective and open to interpretation, while proof is based on objective, empirical data.

How do scientists ensure the validity of their proof?

Scientists use various methods to ensure the validity of their proof, including conducting repeated experiments, peer review, and controlling for variables. They also strive to eliminate bias and consider alternative explanations for their findings. Collaboration and replication of experiments by other scientists also help to validate proof.

Similar threads

Back
Top