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Mathematical Statements

Anonymous Sun 31 Jan 22:36:41 2021 No.12650495 View Reply Original Report

Quoted By: >>12650503 >>12650505 >>12650683 >>12650825 >>12651681 >>12651757 >>12651770

If a mathematical statement is valid, is that the same thing as saying that the statement is true? I am having a bit of a dilemma with regards to the statement "if x is an odd integer, then x + 1 is also odd" apparently being a valid mathematical statement.

Anonymous

Anonymous Sun 31 Jan 2021 22:38:29 No.12650503 Report

Quoted By: >>12650518

>>12650495
>if x is an odd integer, then x + 1 is also odd
that's literally not true

Anonymous

Anonymous Sun 31 Jan 2021 22:38:46 No.12650505 Report

Quoted By: >>12650518

>>12650495
You can have a valid sentence that is incorrect.

Anonymous

Anonymous Sun 31 Jan 2021 22:42:32 No.12650518 Report

Quoted By: >>12650629

>>12650503
The problem is literally:
>The sentence, "If x is an odd integer, then x+1 is also an odd integer." is a valid mathematical statement.

>>12650505
Are we saying grammatically correct but mathematically incorrect?

Anonymous

Anonymous Sun 31 Jan 2021 23:22:22 No.12650629 Report

Quoted By: >>12650650 >>12650723

>>12650518
No he means logically correct but mathematically incorrect. Math only deals with true statements, but logic also deals with false statements

Anonymous

Anonymous Sun 31 Jan 2021 23:30:01 No.12650650 Report

Quoted By:

>>12650629
Why wasn't it stated as a logically valid statement then? If he is asking whether or not it is mathematically valid then the answer is false, but if he is asking whether or not it is logically valid then it should be stated as a logic problem, not a mathematical one.

Anonymous

Anonymous Sun 31 Jan 2021 23:40:29 No.12650683 Report

Quoted By: >>12650691

>>12650495
It's valid. It's wrong, but still valid.
This seems more of a language issue, not mathematics.

Anonymous

Anonymous Sun 31 Jan 2021 23:42:48 No.12650691 Report

Quoted By:

>>12650683
The question is then: What do you mean by 'valid'?

Anonymous

Anonymous Sun 31 Jan 2021 23:51:36 No.12650723 Report

Quoted By:

>>12650629
On the same note... It shouldn't even be logically correct since if A is true and B is false then if then conditional comes out as false.

Anonymous

Anonymous Mon 01 Feb 2021 00:25:45 No.12650825 Report

Quoted By: >>12650852 >>12651245

>>12650495
In the language of math you got some rules to construct valid math statems ( something like a first/second degree logic language )
You can think about your statement as X+1< X for real numbers. This is a valid statement but it is always false. As long as something is not a theorem or something like that, a mathematical expression is valid without being true.

Anonymous

Anonymous Mon 01 Feb 2021 00:35:35 No.12650852 Report

Quoted By:

>>12650825
>As long as something is not a theorem or something like that, a mathematical expression is valid without being true.
I will bite my tongue every time I come across it, but I must accept it if that is just the [spoiler:lit]made up[/spoiler:lit] rule.

Anonymous

Anonymous Mon 01 Feb 2021 02:59:18 No.12651245 Report

Quoted By:

>>12650825
Well, if it was not valid, how could you set up a contradiction?

I tend to use equations as propositions. I take them to some conclusion(s) where either some or all conclusions turn out false. Isn't that common?

Anonymous

Anonymous Mon 01 Feb 2021 06:39:59 No.12651681 Report

Quoted By:

>>12650495
>If a mathematical statement is valid, is that the same thing as saying that the statement is true?
no
a valid statement is simply one that is "well-formed" in that it "makes sense" and can be assigned a truth value (either true or false)

Anonymous

Anonymous Mon 01 Feb 2021 07:22:27 No.12651757 Report

Quoted By:

>>12650495
thanks for this image op

Anonymous

Anonymous Mon 01 Feb 2021 07:39:20 No.12651770 Report

Quoted By:

>>12650495
1+i < 5 is an invalid statement
1 < 5 is a valid statement which is true
5 < 1 is a valid statement which is false

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