Why are direct proofs often considered better than indirect proofs?

Paloma Sanford
2022-10-26
Answered

Why are direct proofs often considered better than indirect proofs?

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Momellaxi

Answered 2022-10-27
Author has **14** answers

A direct proof often provides more information: if, for example, you want to show that there exists a number with some property, then a direct proof is much more likely than an indirect proof to tell you what that number actually is. This is also true for more complicated statements: if you want to prove "For all $x$ there is some $y$ such that [stuff]," you probably also want to know a particular function spitting out such a $y$ for each given $x$. Again, a direct proof is much more likely to provide that information to you.

asked 2022-09-27

Is it possible to prove directly that even perfect squares have even square roots? Or, symbolically:

$\mathrm{\forall}n\in \mathbb{Z},\text{}\text{}{n}^{2}\text{is even}\Rightarrow n\text{is even}$ $\mathrm{\forall}n\in \mathbb{Z},\text{}\text{}{n}^{2}\text{is even}\Rightarrow n\text{is even}$

$\mathrm{\forall}n\in \mathbb{Z},\text{}\text{}{n}^{2}\text{is even}\Rightarrow n\text{is even}$ $\mathrm{\forall}n\in \mathbb{Z},\text{}\text{}{n}^{2}\text{is even}\Rightarrow n\text{is even}$

asked 2022-09-24

Proof the above premises and hypothesis using Indirect proof:

Premise $1$: $P\to \mathrm{\neg}R$

Premise $2$: $Q\to S$

Premise $3$: $(R\vee S)\to T$

Premise $4$: $\mathrm{\neg}T$

Hypothesis: $P\vee Q$

Premise $1$: $P\to \mathrm{\neg}R$

Premise $2$: $Q\to S$

Premise $3$: $(R\vee S)\to T$

Premise $4$: $\mathrm{\neg}T$

Hypothesis: $P\vee Q$

asked 2022-08-06

$A\mathrm{\setminus}B=B\mathrm{\setminus}A\u27faA=B$

can we actually prove it without using contradiction?

can we actually prove it without using contradiction?

asked 2022-11-04

Does ${x}^{2}\equiv 3$ (mod $q$) (where $q$ is an odd prime) have infinite solutions?

asked 2022-10-28

Prove the square root of $2$ is an irrational number.

asked 2022-07-17

How to solve this type of sum using indirect proof. For any real number $x$ , if ${x}^{3}+2x+33\ne 0$ , then $x+3\ne 0$

asked 2022-08-16

Prove if $\{{a}_{n}\}$ $\to $ $\mathrm{\infty}$, then $\{{a}_{n}\}$ is not bounded above. Give an indirect proof.