/sci/ - Science & Math

>>6143474
there

im looking for math-related gifs, such as the one attached
fractals, symmetrical shapes, etc

I have a question about axioms and logical reasoning.

Let's say I made a new mathematical system, and I had one axiom. Could I derive any theorems from this?

If I had two axioms, could I only derive one theorem from this, by combining the two axioms? Obviously I could express the theorem in multiple ways, but would it fundamentally be one theorem?

And then, with <span class="math">n[/spoiler] axioms, can you only derive <span class="math">\sum_{i=2}^ n \choose i =2^{n}-n-1[/spoiler] theorems.

Or can a certain combination of axioms produce more than one theorem? Can they produce infinitely many?

Sorry if any of what I said didn't make sense.

I have a question about axioms and logical reasoning.

Let's say I made a new mathematical system, and I had one axiom. Could I derive any theorems from this?

If I had two axioms, could I only derive one theorem from this, by combining the two axioms? Obviously I could express the theorem in multiple ways, but would it fundamentally be one theorem?

And then, with <span class="math">n[/spoiler] axioms, can you only derive <span class="math">\sum_{i=2}^{n}\binom{n}{i}=2^{n}-n-1[/spoiler] theorems.

Or can a certain combination of axioms produce more than one theorem? Can they produce infinitely many?

Sorry if any of what I said didn't make sense.

>>2466424
>>2466424


i am perfectly human and forever will be.

but i can tell you about space and time if you wish.

complex as we know it life is nothing more than a large domino formed from smaller ones.


the universe is a mass of chaos with a ridiculous amount of matter energy and other nice things like time and dimension spinning and shifting all the time.

life can form outside the filter of evolution in different ways, but im sure life who's origins
lies in the Darwinian evolution algorithm will be plenty and quenching enough for this debate.


look up chaos theory it may blow you away.
anyway, the seed of life is matter and time.

matter in nature has and will always collide, melt, stem, burn, gravitate, implode, explode, and do all those little things matter does that we both do and dont know about.

now with all that movement and energy eventually given enough of Time matter will eventually form in such a way that it can self replicate, it then copies so much that now evolution sets in.

second part in a sec.