What is the difference between injective and surjective proof?
I am trying to understand the distinction between injective and surjective proofs in mathematics. I want to know how they differ in terms of their approach, structure, and the conclusions they lead to.
How to proof an injective?
I'm trying to figure out how to prove that a function is injective. I know it involves showing that every element in the domain maps to a unique element in the codomain, but I'm not sure how to formally demonstrate this.
What is an example of shifting the burden of proof?
Could you provide an instance where the burden of proof has been shifted in a real-world scenario? Imagine a situation where one party, let's say a prosecutor in a criminal case, initially has the responsibility to prove their allegations. However, due to certain circumstances, this responsibility is then shifted onto the defendant. Can you give a concrete example of such a situation, highlighting the specific reasons behind the shift and its implications for both parties involved?
Can you prove something doesn't exist?
Can you truly prove that something doesn't exist, especially in the realm of cryptocurrency and finance? With the ever-evolving nature of technology and the decentralized structure of blockchain networks, it's not always straightforward to definitively state that something doesn't exist. For instance, a new cryptocurrency project may not have launched yet, but does that mean it doesn't exist in the minds of its creators or in the potential it holds? Or, in the case of a lost wallet or stolen funds, how can we be sure they're gone forever and not just hidden or inaccessible? So, is it possible to prove the nonexistence of something in the complex world of cryptocurrency and finance?
What proof is Jefferson's Reserve?
I'm curious, could you elaborate on what proof or evidence does Jefferson's Reserve provide to back up its claims? Is it backed by tangible assets or a robust auditing process? Additionally, what sets it apart from other cryptocurrencies in terms of trustworthiness and transparency? I'm eager to understand the specifics behind this digital asset and its claims of stability and security.