That is, after each natural number is constructed, it actually adds the previous natural number [self] as an element to the set of its [self].

Think about it, 1, 2, 3, 4... are they all like this?

Yes, indeed.

So, now if you add the entire set of natural numbers itself as an element to the set of natural numbers, what will you get?

Give it a try.

Many times, people habitually record the set of natural numbers as N.

However, in the ordinal number theory system, the entire set of natural numbers is usually recorded as w.

Therefore, w can ={0,1,2,3...n}

Then, if w is added to its own set, it is: {0,1,2,3...n...w}

So, is this set well ordered?

Yes, it is a well-ordered set and the real thing.

Because any two elements among them can be compared in size.

And w contains all other elements, and all other elements are also subsets of w.

Therefore, w should be ranked last when sorting.

There is no doubt about it.

In short, the operation of "adding an element to the end of all natural numbers" was finally successful.

The breakthrough for w was finally successful.

The new transfinite ordinal number obtained through this operation is the previous {0,1,2,3...n-1...w}.

That is, w 1.

Note that the 1 here is not the addition of a natural number 1, that is a completely different matter.

At the same time, w cannot simply use the four arithmetic operations of addition, subtraction, multiplication and division. That is a big mistake.

Because the sum of set ordinal numbers is defined after defining a certain well-ordered relationship on the non-intersecting union of two well-ordered sets.

In addition, after obtaining w 1, a larger transfinite ordinal number that cannot establish a one-to-one correspondence with the set of natural numbers.

Then we can get w 2 by repeating the previous operation of adding w to itself to get w 1.

Then add w 2 to itself to get w 3.

By repeating this operation, you can get w 4, w 5, w 6, w 7...

By analogy, after performing an infinite number of such operations, we can reach the limit of this infinite and infinite road - w w.

That is, w·2.

w can be called the first level of infinity, and w·2 can be called the second level of infinity.

In a sense, the gap between the two cannot be described even by the simple word "infinite".

Also note that w·2≠2xw.

w·2 is equal to w w, which is also equal to wx2.

In other words, 2xw≠wx2.

These two are completely different ‘things’.

The latter is a higher-order infinite ordinal number that is much, much, much larger than the natural number set w.

After reaching this level, similar to the previous 'addition' situation, there is no commutative law of multiplication among ordinal numbers.

If we simply interpret w·2 as 2xw, it would also be a big mistake.

Because 2 2 2... keep adding, adding w times in total, the final result will still be w.

In short, after getting w·2, you can continue to use the previous method, infinitely and infinitely to get w·2 1, w·2 2, w·2 3, w·2 4...

By analogy, we finally get w·2 w.

That is, w·3.

Now that we have w·3, we can naturally obtain w·4, w·5, w·6 by replicating the previous infinite and infinite methods... and finally get wxw, which is w2.

This is another higher-order transfinite ordinal number that far surpasses all the previous transfinite ordinal numbers.

At the same time, since we have w2, we can naturally obtain w3, w?, w?, w?... by continuously performing various more complex operations than before.

It finally breaks through to w?, which is w^w, and can also be written as w↑w.

And Mu Cang, and the boundless ocean of time beneath his feet, are exactly in two deep levels that are not too far above the huge transfinite ordinal number w↑w.

It's just that Shi Wangyang's level is lower, and Mu Cang's level is higher.

In short, the gap between the two is not particularly 'big' on the whole.

This is exactly why Mu Cang was able to trample on the endless past and future of the boundless sea so wantonly.

Because in the realm of real infinity, even if there is only a slight difference, it will inevitably be an infinite gap.

In addition, Mu Cang also clearly knows that the power of chaos is not just that.

〖w↑wAbove〗 is definitely not the end of his surge in strength.

There was some kind of power that suppressed Mu Cang and suppressed the chaos of chaos.

"The source of this oppressive power...the Arrow of Meaning."

Mu Cang slowly raised his head and looked at the... huge bronze arrow that existed in the endless distance above the ocean of time.

That's right, it was the mysterious bronze arrow that hung over the endless past and future of the boundless sea - the Arrow of Meaning, that suppressed his growth in strength.

not only that.

Mu Cang could clearly feel that the endless ocean of time below was severely suppressed by this bronze arrow of unknown origin.

If it were not for the suppression of the Arrow of Meaning, the magnitude level of Time Vast Ocean would most likely be elevated by several levels.

But for this arrow of meaning that exuded such terrifying and suppressive power, Mu Cang understood from somewhere that maybe... it didn't deliberately suppress anything or restrain anything at all.

This arrow may still be in some very deep state of 'sleep'.

In other words, the terrifying suppression that Mu Cang and Shi Wangyang endured was most likely just a little pressure naturally exuded by the Arrow of Meaning.

In other words, this mysterious arrow of meaning simply hung there, severely suppressing Mu Cang and the ocean of time.

As a result, Mu Cang was unable to be promoted to the level he was supposed to be promoted to.

It also made the ocean of time fall hard from the level where it should have stood.

However, Mu Cang also has a solution to this problem.

The method is to leave this vast ocean of time.
Chapter completed!