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Line 1: + + − Mathematics includes many practical results concerning quantity and measure, such as calculations involving numbers, financial accounting, geometric construction of building, astronomical calculations, calendar dating, telling time, engineering, physics, chemistry, etc. but also more abstract issues such as establishing the conditions under which certain kinds of equations and formulas have solutions.+ + + + + + − ==Symbols, Equations, and Theories==+ − − Mathematics is expressed with [[symbol]]s. Some of the most commonly used are the numerals 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. These are symbols used to express our intuitive notion of [[quantity]]. Other symbol used in elementary mathematics are the equality ( = ), addition ( + ), subtraction ( - ), multiplication ( x ), less than ( < ), greater than ( > ), etc. More advanced branches of mathematics have their own symbols. − − An [[equation]] is a mathematical statement that asserts the equality of two expressions. Some equations, like (x + 2 = 5), express the equality of two quantities. Other equations, called [[differential equation]]s, express the equality of two [[function]]s. +
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'''Mathematics''' is the rigorous analysis of abstract structures, including numeric and logical systems. The earliest known beginning of this topic is about 2400 B.C., the date of the oldest extant mathematical tablets.<ref>Davis & Hersh, ''The Mathematical Experience'' xi (Mariner Books 1981)</ref>
'''Mathematics''' is the rigorous analysis of abstract structures, including numeric and logical systems. The earliest known beginning of this topic is about 2400 B.C., the date of the oldest extant mathematical tablets.<ref>Davis & Hersh, ''The Mathematical Experience'' xi (Mariner Books 1981)</ref>
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'''Christian apologetics''' is the defense of the [[Christianity|Christian]] faith through logical arguments. The term comes from the [[Greek]] word ''apologia'', which means "defense". The expression "Christian apologist" therefore does not mean that someone is apologising for or on behalf of [[Christianity]] as is sometimes thought, but that he or she is defending and justifying it. There are a <nowiki>f the Bible, and still others in historical or philosophical defenses of Christianity (such as [[Gary Habermas]] or [[Lee Strobel]]). Christian apologist [[JP Holding]] has recommended that prospective apologists choose one area of focus rather than trying to be a "jack of all trades". <ref>http://www.tektonics.org/qt/sowant.html</ref> Some feel that faith alone should ne<nowiki>
ed no justification, however, many feel that Christians should be prepared to defend and spread their faith by intellectual means, especially as many people will not accept Christianity without a "rational" reason to do so.
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==History of Christian Apologetics==
Christian apologetics has existed as long as Christianity itself. [[Jesus]] himself spent time in the temples and synagogues, debating and explaining the meaning of the scriptures. The [[Saint Peter|Apostle Peter]] exhorted early Christians to apologetics, writing,
:"Always be prepared to give an answer to everyone who asks you to give the reason for the hope that you have. But do this with gentleness and respect, keeping a clear conscience, so that those who speak maliciously against your good behavior in Christ may be ashamed of their slander." 1 Peter 3:15-16.
The Apostle Paul also spent time in [[Athens]], debating [[Stoicism|Stoic]] and Epicurian philosophers. Acts 17:16.
Great theologians such as [[Origen]], Athanasius, [[Irenaeus]], [[Martyr]], [[Augustine]], and [[Aquinas]] continued the tradition of apologetics on a dramatic scale. At the same time, apologetics was practiced by countless individual Christians, explaining and defending their beliefs.
A mathematical theory is expressed as a set of sentences, called [[axiom]]s. These axioms should be self consistent, that is, they must not contradict with each other. From these axioms, new results can be derived adhering strictly to mathematical logic. These derived results are called [[theorem]]s. It is important to note that, according to the [[Godel's Incompleteness Theorems]], it is impossible to state a self consistent set of axioms from which the whole mathematics can be derived.
A mathematical theory is expressed as a set of sentences, called [[axiom]]s. These axioms should be self consistent, that is, they must not contradict with each other. From these axioms, new results can be derived adhering strictly to mathematical logic. These derived results are called [[theorem]]s. It is important to note that, according to the [[Godel's Incompleteness Theorems]], it is impossible to state a self consistent set of axioms from which the whole mathematics can be derived.