Tree 3 Number Math

And yet math shows us it exists.

Tree 3 number math. In fact graham s number is practically equivalent to zero when compared to tree 3. Professor tony padilla on the epic number tree 3. Graham s number is a fixed integer. The tree n function returns the longest possible tree made with n elements that follow very specific rules.

Now we are ready to find a lower bound for tree 3. N b 3. P a ii the sum of the two numbers is even. Wrap your head around the enormity of the number tree 3 this number is too large to notate directly too large to comprehend too large for physics to describe.

One vertex with label 3. Let s be the sample space and a be the event that the sum is 4. When the input is 1 or 2 the length of the longest possible tree is small. For practical proof we need advanced techniques such as transfinite arithmetic and ordinal numbers.

When it is 3 the length is very very very long. Https youtu be iihcna9yapk more links stuff in full description below graham s numb. When doing tree 1 and tree 2 it s immediately obvious that the sequence must terminate very quickly but once you start computing tree 3 it seems that the sequence should go on forever as there seems to be. It doesn t increase in size it s just a number.

If we add a path of length m rather than a single child we get a lower bound of tree 2 m 2 n 1. The really laymen explanation for why tree 3 is so big goes like this. Not so much the fact that it s so large which it doubtlessly is but the fact that it somehow manages to be finite as does any other tree number. N a 2.

Tree 3 actually came from kruskal s tree theorem and it is far far bigger than graham s number. That s like saying the number two increases in size or something along those lines. Displaystyle a x 2 uparrow x 1 x. I the sum of the numbers is 4.

Graham s number for example is approximately a64 4 which is much smaller than the lower bound aa 187196 1. A few words of appreciation about tree 3 don t really have much to say about it other than the fact that it s totally mind blowing. Also a small nitpick. Define tree 3 n to be tree 2 n n.

A lower bound for n 4 and hence an extremely weak lower bound for tree 3 is aa 187196 1 where a is a version of ackermann s function. Let c be the event that the product of the two numbers is at least 5. In a nutshell if we use finite arithmetics we can never be able to prove physically that tree 3 is finite. Let b be the event that the sum is even.

These rules guarantee that the resulting longest tree sequence is finite.