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"Stemming" as well as "Lemmatization" are commonly used buzzwords in the field of Information Retrieval (IR), particularly in the development of powerful search engines. [...]

So what exactly is the difference between these two methods? What are the advantages and disadvantages and which one should be preferred? [...]

Some say software developers draw their motivation from minimizing or maximizing numbers in any given problem. That's a smug innuendo. From my experience, developers are always on the lookout for beautiful solutions, of which numbers are but a symptom. The usage of approximative data structures for language processing is one such example of a beautiful idea with nice numbers.