Mathmetical induction

Mathematical induction

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

why in induction problems we assume that f(n) is true and then proceed.....this is only the thing to prove

Shubham Gupta - 7 years, 11 months ago

I would like to explain the whole principle: First we check for $f(1)$ , if it is true we proceed.Then we assume that it is true for a natural number k.Then we check whether it is true for k+1.If it is also true then our given expression is true for all natural numbers.We assumed that it is true for k then we proceed, but previously we checked that it is true for 1.So in this case k=1.Now we prove that it is true for k+1,so it is true for k=2.So now we proved that it is true for 2.Now ,let k=2 as k=2 satisfies the condition,so we again prove that it is true for k+1 i.e 3.Again we let k=3 and prove for k=4.The cycle goes on and on which shows that expression is true for all natural numbers.Let me know where I am wrong.Yes I accept my weak english.Sorry for it.

Kishan k - 7 years, 11 months ago

thnks kevin ,and about your english ,its absolutely flawless

Shubham Gupta - 7 years, 11 months ago

You are referring to the First Principle of Finite Induction, which can be proved by contradiction.

Calvin Lin Staff - 7 years, 11 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$