Welcome to into infinity. Today we will be discussing the nature of ordinal numbers, cardinal numbers, and the structure of infinity. Sounds complicated. Not really actually, it’s something we use every day. Let’s have a look at some of the number categorizations that we have, and see how they fit into the structure of infinity. And that way we can discard Asians that don’t fit into the necessary categorization in order to understand the infinite. So to begin with, let us understand the difference between an ordinal and a cardinal number. an ordinal number is something that is ordered in time. For example, I know that the first, second, third, fourth, and fifth are all ordinal numbers, they are taking steps in a direction in a theory of effort that we have. This is called the number of steps is determined by the number e, and it starts at zero, which would be zero effort. And we take them where they sit within the infinite matrix of numbers space, we can then go on to try and decipher how that works with the creation of number space to begin with. Let us begin by considering an infinite is worth of infinity. Now that’s a little bit of a tough concept, but we write that in mathematics is just infinity to the power of infinity to the power of infinity to the power of infinity, apparently infinity on an on to infinity. This concept might be relatively difficult to wrap your head around, but luckily, we don’t need to get to the end, we just need to know that the concept is there. When we look at infinite sets, what we’re really doing is abstracting from the infinite set a certain number of infinities. The number of infinities can be determined by subtraction, ie what is not what is missing. And as we have already stressed that the ordinal numbers are missing the number zero and all of the negative numbers. However, ordinal numbers also have a place within the creation of infinity. For example, there is a first step, the first step to creating numbers is actually to divide infinity. The division of infinity creates two infinities doubling the infinite space. However, in accordance with mathematical law, we understand that when we divide something equally, we will get to equal parts. One part we call negative infinity, a second part we call positive infinity, between negative and positive infinity, we have the number zero. When we focus in on this space, we find that actually the number zero itself operates with a polarity. For example, we can take any number between one and zero and which we call the reciprocal value, and we will find it begins with the number zero point followed by an infinite fraction. Once we have realised this, we realise we must place a positive in front of that zero in order to complete the identification of that number as a
Please to its negative counterpart on the negative side, which must be applied negative zero in front of the infinite fraction. As we reduce in size towards zero, we realise that positive zero and negative zero never change. Therefore, there is an infinite set we call positive zero and an infinite set with negative zero, which also are outside of the cardinal numbers. Three, which are also outside of the ordinal numbers, they are also not reachable by the cardinal division, and therefore, they are containers of cardinal numbers, zero plus zero to plus infinity, is one set of cardinal numbers. And the second set of cardinal numbers is minus zero to minus infinity. And it’s upon this basis that all number functions can now become operable. Once we have this structure in place, functions such as addition, and subtraction can become fully operational, before this point mathematics cannot exist. It is the structure of mathematics upon which we based on logic. So, let us now place this into an equation so that we can understand this more clearly. If we take the first division, which means the infinity divided by the number one, which is the ordinal, number one, then we get the number zero. And we near we realise that that divides that zero into five distinct types, sorry, three distinct types, a plus zero, a 00, and a negative zero. We notice this phenomena,with the folk with the proton neutron configuration found at the centre of each atom. For this reason, this is more than just a curiosity. Additionally, we find that the space around us all of this contains an infinite set of numbers from one, we can count as the ordinal numbers. Sorry, one, zero to one, one set of cardinal numbers in the positive and zero to one, one set of cardinal numbers in the negative two sets of infinity. We can draw this as his two circles that are connected at a point. And by zooming into that point, we can draw the number plus zero and negative zero and place a line through the two circles to represent the outer edge of the infinite. What we are seeing here is that the outer edge of the infinite really, we call pi joins itself to the infinity and to complete a complete cycle of Cardinal positive numbers. So we can rotate to the 01 180 degrees around the circumference of pi. We can also rotate the same on the other side and unify the number one and zero, create the infant trade number infinity and zero and create a container for infinite space, which we call reciprocal space. Notice then that we have a reciprocal space that is contained by the number zero at the centre, positive one on one side, negative one on the other side, and is divided and we will examine how this space becomes divided into smaller sections to manifest various different aspects of quantum number space.