1947 the author has dedicated this book to the millions who long for proof that their loved ones live on forever. There is proof that is true to those who can understand.

Much may be gathered, indirectly, from the arguments in these pages, as to the real nature of the Earth on which we live and of the heavenly bodies which were created for us. The reader is requested to be patient in this matter and not expect a whole flood of light to burst in upon him at once, through the dense clouds of opposition and prejudice which hang all around. Old ideas have to be gotten rid of, by some people, before they can entertain the new; and this will especially be the case in the matter of the Sun, about which we are taught, by Mr. Proctor, as follows: “The globe of the Sun is so much larger than that of the Earth that no less than 1,250,000 globes as large as the Earth would be wanted to make up together a globe as large as the Sun.” Whereas, we know that, as it is demonstrated that the Sun moves round over the Earth, its size is proportionately less. We can then easily understand that Day and Night, and the Seasons are brought about by his daily circuits round in a course concentric with the North, diminishing in their extent to the end of June, and increasing until the end of December, the equatorial region being the area covered by the Sun’s mean motion. If, then, these pages serve but to arouse the spirit of enquiry, the author will be satisfied.

This book is an introduction to the language and standard proof methods of mathematics. It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity.

Many students have trouble the first time they take a mathematics course in which proofs play a significant role. This new edition of Velleman's successful text will prepare students to make the transition from solving problems to proving theorems by teaching them the techniques needed to read and write proofs. The book begins with the basic concepts of logic and set theory, to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for a step-by-step breakdown of the most important techniques used in constructing proofs. The author shows how complex proofs are built up from these smaller steps, using detailed 'scratch work' sections to expose the machinery of proofs about the natural numbers, relations, functions, and infinite sets. To give students the opportunity to construct their own proofs, this new edition contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software. No background beyond standard high school mathematics is assumed. This book will be useful to anyone interested in logic and proofs: computer scientists, philosophers, linguists, and of course mathematicians.

Do you want to experience God realities in your life? Pastor, author, and entrepreneur Pat Cannon unpacks an often overlooked truth regarding our relationship with God. Words are cheap. Unless you back them up with action, they don't mean much. Love God Love People Prove It will teach you how to shift from dabbling in Jesus to following Him. Is it easy? No. Is it worth it? Absolutely!

This book was impressed on me by the Lord, to wright these messages in poetic form. Never did anything like this in my life. As God would give me little titles I would wright them on paper which I kept in my pocket. Then most times within a week or two it would end up as a sermon in poetic form. This book covers multiple subjects which each of us face in life. This book is designed for whoever reads this book, to cause you to think things out, and then to form your own thinking as how God would have you process it. The emphasis of this book is to read and study it with an open mind, as you study the scriptures on your own. The reason there are few scriptures in this book is to cause you to want to search the scriptures yourself, to prove whether it is right or wrong. That is why God’s word informs us in 2 Timothy 2: 15, “Study to show thyself approved unto God a workman that needeth not to be ashamed, rightly dividing the word of truth.” This scripture informs us that we are to study God’s word in order to find what God requires of us, what he empresses on our heart as taught by Jesus to us in Matthew 25: 14-30. When we read and study God’s Word, read it with an open mind, asking him what he has for you today. We will never know it all, for we will keep learning till Jesus comes, or we leave this earth. Never allow people to put a guilt trip on you that you must know it all.

There is much unfairness, inequality and suffering in our world. Could some of these situations be the direct result of actions we took in past lives? This book provides a series of spirit communications received through spiritual mediumship indicating that to be true. Spirits in the afterlife reveal reasonable explanations why many seemingly unexplained human conditions, people and many tragic circumstances in our lives were brought about as a consequence of our choices and actions made in past life existences. Also revealed, is that we chose and were aware, before rebirth, what the circumstances of our lives would be. For we returned to earth, out of love: to make amends, for redemption, self-sacrifice in caring for those we love, as well as for the spiritual progress of our soul. Further, we are not alone in our journey throughout our material lives. We have our spirit guides and the spirits of family and friends that help us from the afterlife, always providing inspiration, guidance and consolation. We are never alone in our sorrows! The life stories herein will provide new insight and answers to the whys of our lives, individually and collectively, and the spirits reveal there is a Divine Plan which is one of CONSOLATION, HOPE and UNCONDITONAL LOVE.