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es between them. Finite and Infinite SetsThere was once a mathematician called Georg Cantor who created a new branch of mathematics called set theory in the late 19th century. Set theory involves collections of numbers or objects. Here's a set:Are these sets of the same size? Yes, they are. This is because they both have five elements. As we will see later, this method of comparing sizes does not work for all sets. An alternate method for comparing set sizes is to match elements of sets in a one one fashion. Think of a small child who wants to compare the number of marbles she has with her brother's collection. Let's say she doesn't know how to count beyond ten. She can still compare the sizes of their collections of marbles by lining up their marbles in two parallel lines. The line on the left contains her marbles while the one on the right contains her brother's. If each marble on the left is aligned with exactly one marble on the right, then they both have the same number of marbles. We can use the same idea to compare infinite sets. If we can find a way to pair up one member of set A with one member of set B, and if there are no members of A without a partner in B and vice versa then we can say that set A and set B have the same number of members.
a journey back in space and time recently, logging more than 1,800 miles in a rented Dodge to attend my 40th class reunion in Kearney, Neb. , a surprisingly robust town of 30,000, where I grew up in the '50s and '60s. But come we did. The 95 or so of us that attended this once a decade Brown Air Force Sneaker
on, the inner magnet's draw irresistible. I wonder why are the bonds between us still so strong after 40 long years? I believe it has to do with the power of a shared block of experiences, experi.
We want to know if the sets and have the same size. We can create the following matching. 678910Let Set N be all counting numbers. N is called the set of natural numbers. 1,2,3,4,5,6,. and so on. Let Set B be the negative numbers 1, 2, 3, . and so on. Can the members of N and B be paired up? The formal way of saying this is "Can A and B be put into a one to one correspondence"?Obviously the answer is yes. 1 in set N corresponds with 1 in B. Likewise:1 13 3and so on. Here, the one one function that maps from A to B is . So useful is the set of counting numbers that any set that can be put into a one to one Black Air Force 1 Low correspondence with it is said to be countably infinite.
event almost universally agreed that we were almost pulled back to our hometown by some primal, mysterious inner magnet. In a small sense, we were like the Jews of the Diaspora drawn back to Israel after World War II. The old ties beckoned; we answered the call. For me, it was beyond logic, intellect and reason. I just knew I was supposed to be there and adjusted my schedule accordingly. I had it easy four pleasant days of travel along well maintained interstates. A few of my fellow pilgrims dodged tornadoes on the road back. One even found herself hiding in a farmhouse cellar for a time with complete strangers, then continuing Nike Air Force 1 High On Feet
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