Cryptocurrency Q&A
What is an example of not injective?
What is an example of not injective?
PulseRider
Thu May 23 2024
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7 answers
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Could you please explain what is meant by "not injective" with a concrete example? I'm having a bit of trouble grasping the concept. Could you illustrate it with a simple scenario or mathematical function that is not injective? It would be helpful if you could also explain why it is not injective and how it differs from an injective function. I'm particularly interested in understanding the consequences of a function not being injective and how it affects the mapping between input and output values. Thank you in advance for your clarification.
7 answers
Andrea
Sat May 25 2024
In the realm of functions, the concept of injectivity plays a crucial role. A function that fails to be injective exhibits a phenomenon known as a "collision" within its range. This collision signifies that two or more distinct inputs map to the same output.
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BitcoinWizardry
Sat May 25 2024
Consider the function f(x)=x2f ( x ) = x^2, which maps real numbers to real numbers. This function is not injective, as it exhibits a collision in its range. Specifically, for any given non-zero real number x, both x and -x produce the same output when squared.
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CryptoAlchemy
Fri May 24 2024
BTCC's wallet service also benefits from the principles of injectivity. Wallets must accurately track and manage cryptocurrency balances, preventing any duplication or overlap of funds.
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Eleonora
Fri May 24 2024
The non-injective nature of f(x)=x2f ( x ) = x^2 can be observed by noting that f(−x)=f(x)f ( -x ) = f ( x ). This equality demonstrates that negative and positive values of x, which are distinct inputs, result in identical outputs when squared.
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Bianca
Fri May 24 2024
This collision has significant implications in the context of cryptocurrency and finance. In these fields, injectivity is often desired to ensure uniqueness and prevent duplications or overlaps.
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