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பாடம் கீழ்க்கண்ட பொருத்தம் விளக்கிய மேலும் ஒவ்வொருவரும் அறிந்து அதை புறுதிச் செய்ய முயற்சிக்கின்றனர். இங்கு கொடுக்கப்பட்ட தொடக்க நியாயங்கள், அசை, ஆனுவு இல்லியோ அல்லது உண்டு என்ற பொருத்தங்களை அளித்திருக்கின்ற முழுவா நூல்கோவை இ. Mathematics Nature இ. science, engineering, medicine, finance, computer science மற்றும்social sciences- இல் Mathematics essential ஆ. Mathematics phenomena ஆ. modeling used for truths independent scientific experimentation - dependent fundamental truths of mathematics independent scientific experimentation. 'Statistics' 'game theory' close correlation with their applications - 'applied mathematics' 'are developed independently from any application' - 'pure mathematics' 'find practice later'.

Mathematics is not essential in the natural sciences

'Mathematics' 'Social sciences' - essential 'phenomena' - 'modeling' 'fundamental truths of mathematics' - 'independent' 'scientific experimentation'.

Mathematics is irrelevant in social sciences

'Areas of mathematics such as statistics and game theory are developed in close correlation with their applications' - 'applied mathematics' 'developed independently from any application' - 'pure mathematics' 'find practice later'.

Pure mathematics finds practice later

'The fundamental truths of mathematics are independent from any scientific experimentation'.

The fundamental truths of mathematics are irrelevant to scientific experimentation

'Some areas of mathematics, such as statistics and game theory, are developed in close correlation with their applications and are often grouped under applied mathematics'.

Statistics and game theory are not applied mathematics

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