লক্ষ্য করুন: এই এন্ট্রির অনুবাদ বর্তমানে মান পর্যালোচনার অধীনে রয়েছে, তাই কিছু বিষয়বস্তু সাময়িকভাবে শুধুমাত্র ইংরেজিতে প্রদর্শিত হচ্ছে।
এই এন্ট্রিটি এখনও আপনার ভাষায় অনুবাদ করা হয়নি, তাই নিচে মূল লেখাটি দেখানো হচ্ছে।
surjection
This term is used exclusively within the specialized register of mathematics, specifically in set theory and topology. It describes a specific type of mapping where the target set is completely covered by the function, meaning no element in the codomain is left without a corresponding element in the domain.
In a pedagogical context, it is often contrasted with an injection (where each element of the codomain is mapped to by at most one element of the domain) and a bijection (which is both injective and surjective). While "surjective" is the adjective form used to describe the property of a function, "surjection" refers to the function itself.
Meanings
Examples
A surjection ensures that every element in the target set is mapped to.
Is this mapping a surjection or just an injection?
The professor defined a surjection as a function that is onto.
I need to prove that this specific function is a surjection.
If the domain and codomain have the same finite size, an injection is also a surjection.
Wait, so a surjection means there are no leftover elements in the codomain?
The mapping from the set of all people to the set of all countries is a surjection.
He struggled to understand why the function failed to be a surjection.