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--- tanszek:oktatas:techcomm:information_-_basics:sciences [2025/09/08 19:42] – [Deductive Sciences] knehez
+++ tanszek:oktatas:techcomm:information_-_basics:sciences [2025/09/15 17:52] (current) – [Inductive Sciences] knehez
@@ Line 1: / Line 1: @@
 ====== What is science? ======
-According to the definition: //Science// is understood as a provable and fact-based system of the objective relationships between //nature//, //society//, and //thinking//.
+According to the definition: //Science// is understood as a provable and fact-based system of the objective relationships between //nature//, //society//, and //human thought//.
-//Science// is not just a collection of knowledge, but a **discovery process**. //Science// aims to discover new information, facts, and answers about our world or the universe.
+However, science is not only a set of theories stored in textbooks. It is a dynamic process of exploration and innovation that directly shapes technology, industry, and daily life. Science is the reason we can design sustainable energy systems, create AI-powered applications, or even send rockets into space.
+//Science// is not just a collection of knowledge, but an ongoing **discovery process**. It aims to discover new information, facts, and answers about our world or the universe, while also solving real-world engineering problems.
 Science, among our historically established forms of social consciousness, is distinguished and emphasized by the following characteristics.
-  * they possess high-reaching concepts or logical tools to formulate or express broad, general or universal **principles** or **laws** (e.g. gravity, axioms, [[https://en.wikipedia.org/wiki/Maxwell%27s_equations|Maxwell's equations]])
+  * It possesses high-reaching concepts or logical tools to formulate or express broad, general or universal **principles** or **laws** or **axioms** (e.g. gravity, axioms, [[https://en.wikipedia.org/wiki/Maxwell%27s_equations|Maxwell's equations]])
-  * they can describe the objective **conditions** under which these principles or laws will prevail.
+  * It can describe the objective **conditions** under which these principles or laws will prevail.
+  * It provides logical methods and computational tools that enable us to calculate, simulate, and predict **results** under specific circumstances.
-  * they possess the required logical tools or methods that can help us to calculate or predict **results** in given circumstances,
+From a modern engineering viewpoint, these features mean that science is not abstract—it is applied, testable, and useful. Every time an engineer uses mathematical models to optimize a production line, simulates a digital twin of a factory, or analyzes big data to predict outcomes, they are applying these scientific principles.
-According to **principles**, **conditions** (circumstances), and **results** (these three general aspects) we can categorize every scientific problem into the following problem groups.
+According to the three general aspects — **principles**, **conditions**, and **results** — we can categorize every scientific problem into the following groups.
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 $$ 1 + 2 + \cdots + k = \frac{k(k+1)}{2}. $$
+Then for \(n = k+1\):
+$$ 1 + 2 + \cdots + k + (k+1) = \frac{k(k+1)}{2} + (k+1). $$
 **Simplify**:
-$$ \frac{k(k+1) + 2(k+1)}{2} = \frac{(k+1)(k+2)}{2}. $$
-Thus, the formula also holds for \( n = k+1 \).
+$$ \frac{k(k+1)}{2} + (k+1) = \frac{k(k+1) + 2(k+1)}{2} = \frac{(k+1)(k+2)}{2}. $$
+Thus, the formula also holds for \( n = k+1 \). Thus, by mathematical induction, the formula holds for all \(n\in\mathbb{N}\)
 https://en.wikipedia.org/wiki/Mathematical_induction