1)"^" means to the power of/to the ______ effect/to the effect of______/to the _____ extent/ to the degree of____/to the _____ degree/to the extent of______/the product of it(future) and itself(now) times ________,etc.
2)"/"/other/over/relating to/relative to/compared to/proportioned/mutually relates to in the fact of relating to,etc., means divide
3)"+"/plus/positive/and,etc., means add
4)"x"/times/of/by/through/because of/applied _____ times,etc., means multiply
5)"-"/minus/negative/from,taking ____ away from/taking away______ from,etc., means subtraction
6)"=" means, can equal/is viewed in equillibrium as/is known as,etc.
F(x) #1 =/= F(x) #2,but F(x) #2 is different only because of where it is located relative to f(x) #1,(underneath 1).
Variations will be marked by inverse of function. x= [f(x)/1][ 1/f(x)] or
x=[f(x)]^1[f(x)]^-1
x can equal part of x by x relating to (part of x through *the mutual degree of its inverse* OR *the mutual degree of its other*).
x is the same as a part of x in the sense that: x=f(x) conditionally
You could even go as far as saying f=part, and x=whole,and the logical product would be:
"Whole is the same as parts of a whole."
In which case we really begin to see how much the validity of a statement depends on context it was said in and the definitions that are being referred to. We could define "is" as meaning "equals conditionally".
In language, if x=all and f=parts, this is using logical syntax,but the meaning may conditionally seem to contradict itself. Mathematically,this equation is potentially logical.
You can take it a step further and replace variables,as long as you are consistent in placing the replacement relative to the general change you wish to make and in all degrees where it should logically apply according to the initial rules of the equation.
Examples:
1=[f(1)][1/f(1)] vs. x=[1(x)][x/1(x)]
2=[f(2)][1/f(2)] vs. x=[2(x)][x/2(x)]
3=[f(3)][1/f(3)] vs. x=[3(x)][x/3(x)]
If 6=unknown(x) and 6=1x2x3,
6=x[f(1)]x[1/f(1)]x[f(2)]x[1/f(2)]x[f(3)]x[1/f(3)] / x[1(x)]x[x/1(x)]x[2(x)]x[x/2(x)]x[3(x)]x[x/3(x)]
6/x=[f(1)][1/f(1)][f(2)][1/f(2)][f(3)][1/f(3)] / [1(x)][x/1(x)][2(x)][x/2(x)][3(x)][x/3(x)]
and potentially,
x/6=[1(x)][x/1(x)][2(x)][x/2(x)][3(x)][x/3(x)] / [f(1)][1/f(1)][f(2)][1/f(2)][f(3)][1/f(3)]
x=6[1(x)]6[x/1(x)]6[2(x)]6[x/2(x)]6[3(x)]6[x/3(x)] / 6[f(1)]6[1/f(1)]6[f(2)]6[1/f(2)]6[f(3)]6[1/f(3)]
and you'd even still come right back down to
x=1/1
the unknown must be 6.
Equations are odd because they are depicting similarity and difference at the same time. They depict abstract coherency(the bigger picture considering seen and unseen),but seem illogical without considering the whole(when focusing on specific parts and comparing them,assuming those parts are the whole). The smaller the field of focus,the more meaning we're able to give to specific variables and the less objectively logical they are to focus on, but...
The point is,so long as x and f are not directly(in every way) related in value, the equation remains logically correct.. Denotation,or the definition of a word, IS connected to logic,and some meanings in a particular denotation are more logically correlated than others on subjective levels,making them more or less valid depending on the process of logic that was used. The more closely two equations are related(smaller total of different variables being considered),the more logical the equation *seems* at a glance,but that doesn't mean the equation is more or less logical. Logical predictions should remain consistent with the actual outcomes if a revised equation follows the same conditions.. however.. logically,shouldn't two seperate terms have a difference if they are technically different,even if the difference is just in spelling? To some people they appear to have a bigger difference than they do to other people.. It's all relative to an individual's past experience and genetic predisposition(Weber's Law,Abolute Threshold,Just Noticeable Difference and Difference Thesholds). This is how we form a more solid perception/illusion of difference/belief system/schema to discriminate with. The bigger the percieved difference,the easier to discriminate,the less personal risk of ambiguity.. The smaller the ACTUAL(objective) difference,the more illogical contradictions to our logic seem,but the more frequently they occur.. unfortunately,the smaller the difference,the more frustrated we tend to get when looking for logical discrepancies.
When dealing with critical thinking,you can also decide how an equation should be adapted by focusing on the relationship of the given variables to each other. In the initial equation, f is apart of x,but x could also be a part of f.. then,based upon definition,you think of two words sharing that relationship and insert them as variables to an equation..
Basically,you consider the rules of an equation exactly the same as the rules of an analogy.. They are the same.
This may seem peculiar,but think about it.. If a rung is considered a part of a ladder, the understanding of a ladder is a necessary part of the comprehension of the concept of a rung. Without it,we could only try to relate it in the terms of our own schema..
Paradoxes do exist. It is a matter of fact,but they don't make sense.. just because things don't make sense doesn't mean they don't exist. Usually what makes them seem strange is that they invalidate a previous assumption. Oxymorons exist in language, and the examples given above are great examples of how they are formed.. Paradoxes exist because not all truths are universal,and some are,in fact,conditional. To let the truth be known,the condition of x being a consistent variable must be met.. Otherwise we simply don't acknowledge them as ever having existed because it is impossible to.. It's impossible to understand something we haven't experienced,because truth is what we do experience in living. Truth is all sensation we percieve,and it is validated within ourselves,or not,but even as we decide they are or are not validated,we are validating them.. giving them meaning,discriminating. We are semantic entities.. we could not "survive" in any other way,because we would not know of our survival.
In this same way,we can view any whole.
Any whole can equal part of any whole by any whole relating to part of any whole through the mutual degree of its inverse or the mutual degree of its other/discriminated part.
A ladder can equal a rung by the ladder relating to the rung of the ladder through the mutual degree of difference.
So why,you may ask,is this significant? Well..
When you think about the all the wars that've ever existed in the world and how many lives have been lost,how many times were those losses the product of contradicting beliefs? How many people have been oppressed,lied to,misinformed,disabled by the situation they were in,and limited in what portion of the world they could experience at any given second? We all are limited in our own unique ways,but some people choose to limit themselves more than others(without knowing it). Some people turn to bullying after growing weary of trying to compromise with reason,they use faulty logic to justify the destruction of others' lives founded on self-righteousness, and still cite no mistake to acknowledge or learn from. But once you have heard you must heed.. so while those people continue down a self-destructive path,I would love for their children to have the option of trying to reach truth from a logical perspective,too.. Everybody has the choice,but not everybody is born with the option.. So I'd gladly enable understanding of percieved differences in intention..
...maybe one day we'll all wake up and understand that our humanity isn't to blame and that through being validated by the fact of their mutual existence, our perceptions are valued the same.
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