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Maiko's Musings


maikochan

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Just had a thought while in the shower that I wanted to write down, even though it's pretty trivial. I'll just use this spot for any thoughts I get that I'd like to share, though likely not important ones.

Anyway, on to the inaugural musing.

Is Zero an Even Number or an Odd Number?
Yes, I know this is a pretty simple argument in number theory, and a pretty trivial one in general, but hey, I wanted to practice some logic.

So, this question has two parts, first, if the number Zero is Even, and second, if it's Odd. Let's tackle the first part, well, first.

First we need to establish what an even number is. I've come up with three criteria as follows: Using Integers for simplicity and because I'm not entirely sure of how fractional or irrational numbers are defined as even or odd.
  1. If a number divided by two produces an integer answer, then the number is even. Formally: X is an integer. If X/2 is an integer, then X is even.
  2. If a number is multiplied by any other number, and the result creates an integer when divided by two, then the first number is even. Formally: X is an Integer. Y is an Integer. If (X*Y)/2 is an integer, then X OR Y is even. (Logical OR) This can also be read as: If (X*Y) passes criteria #1, then X OR Y is even.
  3. Integers alternate between even and odd as one progresses along the number line. If a number can reach the number two by adding or subtracting in multiples of two, then the number is even. Formally: Not going to try this as it would require induction, which I'm not so great at.
With these criteria, we can assess whether Zero is Even.

First: If Zero is divided by two, is the result an integer?
Yes. Zero is an integer (by convention). Zero divided by any number results in Zero. Formally, 0/X = 0. As Zero is an integer, criteria #1 is met.

Second: If Zero is multiplied by any number, will the resultant number pass criteria #1?
Yes. Zero multiplied by any number results in Zero. Formally, 0*X = 0. As Zero is shown to pass the criteria #1, Zero also passes criteria #2.

Third: Can the number two be reached by steps of two from Zero?
Yes. Simply adding two to Zero results in two. Formally 0+2=2. Thus criteria #3 is met.

From these criteria we can conclude that Zero is an even number.

To determine if Zero is an Odd number, we can assume that no number can be both even and odd, and since we have proven that Zero is an even number, Zero cannot be an Odd number.



So that's that. Any number theorist or a university student who is even tangentially involved with mathematics could probably point to any number of problems with my proofs. But it's been a couple of years since I did any proofs like this, and it just felt good to go through the motions, as it were. And again, the result is trivial, but it's the journey, they say, and not the destination, that matters.

I welcome any input on this or any other musing I post. For now, Maiko out.
 

Mamono Assault Force

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Re: Maiko's Musings

Zero being an even number is pretty well recognized by most. It's strange to group Zero in with other even numbers because Zero destroys all creation when it divides, and it's a pretty strange number altogether to work with.

But by definition, Zero fits the bill.
 
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maikochan

maikochan

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Re: Maiko's Musings

Some campaign setting and house rule ideas I want to put down. Comments appreciated. House rules will be aimed at Pathfinder.

HP Strain-
Strain is another form of non-lethal damage. It stacks with non-lethal damage for determining whether a character will be unconscious or otherwise impaired. That is, if a character takes 8 points of non-lethal damage, then takes 4 points of Strain, they would be considered to have taken 12 points of non-lethal damage.

Strain isn't reduced over time, however. It can be removed by healing magic (or other forms of HP restoration such as Fast Healing), in which case it is considered to be non-lethal damage for the purposes of healing. Strain is removed after any non-Strain non-lethal damage is removed.
Strain can also be removed through the application of the Heal skill. A character can attempt to remove Strain with 1 minute of work and a DC 15 Heal check. Success removes a number of points of Strain equal to the healing character's ranks in the Heal skill. Attempting to use this application on yourself raises the DC to 20.
Strain is also removed after resting. 8 hours of rest completely removes all Strain damage the character has taken. Time spent unconscious due to non-lethal damage doesn't count towards this.
Strain is also reduced when a character is knocked unconscious. When unconscious, Strain is reduced at the same rate as normal non-lethal damage (1 point of damage per character level per hour).

Characters gain Strain by using actions that specifically cause it to accrue. The main use is to Endure damage.

Endure Damage-
When a character is dealt normal damage, they can, as an immediate action, convert all of the incoming damage to Strain damage. A character can only convert all of the incoming damage, not a portion of it. Characters with no Constitution score (Constructs and Undead), with no Intelligence score (Oozes and Vermin), or with the Mindless trait, or otherwise immune to non-lethal damage cannot use Endure Damage.

Design notes-
HP Strain and Endure Damage are meant to be a way to make combats less lethal, without making it trivial to heal between battles. With Strain, resting or healing is still necessary if the party takes heavy damage. If it were converted to non-lethal, they could wander around in safer locations doing things while they waited for it to go down. Really though, this is meant to be used with the Non-lethal Gradient below.
It's also good for coming up with attacks or other abilities that cause fatigue in the users. Rather than setting a hard limit on how many times a day an ability can be used, excessive use can instead cause Strain, which would necessitate the character weighing whether it would be worth it to use the ability or save their strength.
Another use could be for "pushing" oneself to gain a bonus on some difficult task (this should never be a form of attack or defense), like holding on to a rope until help arrives or pouring over documents in order to find a clue.


Non-lethal Gradient-
A variant way of handling non-lethal damage that allows for a character to stay active for a bit longer. Normally, when a character's non-lethal damage exceeds their current HP, they fall unconscious.

With this variant, when a character's non-lethal damage exceeds their current HP, the character becomes staggered (able to take only a single standard or move action per round) until their current HP exceeds their non-lethal damage.
When a character's non-lethal damage exceeds their maximum HP, they need to make an immediate Fort save (DC 10+non-lethal damage above their max HP) or fall unconscious. Success means the character is staggered. The character must then make the same Fort save at the start of each of their turns until their non-lethal damage is reduced, or they fall unconscious. If a character takes a standard action while their non-lethal damage exceeds their maximum HP, they must make an immediate Fort save with the same DC before completing the action, or fall unconscious.
After falling unconscious, a character can continue to take non-lethal damage up to twice their maximum HP. After that, any further non-lethal damage is converted to normal damage.

Design notes-
Combined with HP Strain, this makes it so that combat remains balanced while making sure that a party wipe doesn't necessarily end with everyone dead without requiring the GM to do any fudging. It also makes it so that characters can keep acting after taking a mix of lethal and non-lethal damage, which should help with any complaints about "I have 1 HP left, but I can keep fighting like I was fully healed!". The Fort saves to stay conscious are also in line with some more heroic actions such as those who cling to consciousness in order to crawl to safety or take out an enemy.
 
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