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tanszek:oktatas:techcomm:information_-_basics:sciences

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tanszek:oktatas:techcomm:information_-_basics:sciences [2025/09/08 19:40] – [Inductive Sciences] kneheztanszek:oktatas:techcomm:information_-_basics:sciences [2025/09/08 19:42] (current) – [Deductive Sciences] knehez
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 According to **principles**, **conditions** (circumstances), and **results** (these three general aspects) we can categorize every scientific problem into the following problem groups. According to **principles**, **conditions** (circumstances), and **results** (these three general aspects) we can categorize every scientific problem into the following problem groups.
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 ====== Inductive Sciences ====== ====== Inductive Sciences ======
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-**Example 2**: Sum of consecutive natural numbers +**Example 2**: Sum of consecutive natural numbers. **Claim**:
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-Claim:+
  
 $$ 1 + 2 + \cdots + n = \frac{n(n+1)}{2}. $$ $$ 1 + 2 + \cdots + n = \frac{n(n+1)}{2}. $$
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 so the statement holds. so the statement holds.
  
-Inductive step:+**Inductive step**:
  
 Assume the formula is true for \(n = k\): Assume the formula is true for \(n = k\):
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 $$ 1 + 2 + \cdots + k = \frac{k(k+1)}{2}. $$ $$ 1 + 2 + \cdots + k = \frac{k(k+1)}{2}. $$
  
-Simplify:+**Simplify**:
 $$ \frac{k(k+1) + 2(k+1)}{2} = \frac{(k+1)(k+2)}{2}. $$ $$ \frac{k(k+1) + 2(k+1)}{2} = \frac{(k+1)(k+2)}{2}. $$
  
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 https://en.wikipedia.org/wiki/Mathematical_induction https://en.wikipedia.org/wiki/Mathematical_induction
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 ====== Deductive Sciences ====== ====== Deductive Sciences ======
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 The quote from [[https://en.wikipedia.org/wiki/Niels_Bohr|Niels Bohr]], //"In the Institute, we only have one piece of experimental equipment: a ping-pong table"// is a good example of reductive reasoning in science. It suggests that groundbreaking discoveries can be achieved not through extensive experimental setups but rather through the adjustment of theoretical laws and conditions. Bohr highlights the power of thought experiments and abstract reasoning, emphasising that manipulating underlying principles can lead to new insights without always needing physical experimentation. The quote from [[https://en.wikipedia.org/wiki/Niels_Bohr|Niels Bohr]], //"In the Institute, we only have one piece of experimental equipment: a ping-pong table"// is a good example of reductive reasoning in science. It suggests that groundbreaking discoveries can be achieved not through extensive experimental setups but rather through the adjustment of theoretical laws and conditions. Bohr highlights the power of thought experiments and abstract reasoning, emphasising that manipulating underlying principles can lead to new insights without always needing physical experimentation.
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 ====== Reductive Sciences ====== ====== Reductive Sciences ======
tanszek/oktatas/techcomm/information_-_basics/sciences.1757360427.txt.gz · Last modified: 2025/09/08 19:40 by knehez