Metamath and Generalized Continuum Hypothesis

Metamath and Generalized Continuum Hypothesis
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Metamath is a computer language for representing mathematical proofs, with various databases and proof assistants. The Generalized Continuum Hypothesis (GCH) posits an intriguing relationship between infinite cardinals and ordinals. Explore how GCH implies the Axiom of Choice (AC) and the implications of a local version of GCH proposed by Specker.

  • Metamath
  • Generalized Continuum Hypothesis
  • GCH
  • Axiom of Choice
  • Mathematics

Uploaded on Apr 29, 2025 | 0 Views


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  1. Al-Mustaqbal University College Anesthesia Techniques Department Vitamins LECTURE Article teachers M.sc. Zainab Mohsen F.I.C.M.S Path Dr. Ammar Hatem

  2. Introduction of Vitamins Organic molecules, essential for the normal growth and development, required in tiny amounts Most of them cannot be synthesized by mammalian cells, must be supplied in the diet

  3. The Classification of Vitamins 1- Water-soluble (Vitamins Bcomplex and C) thiamineVB1, riboflavinVB2, niacin VB5 , VB6, biotin cobalaminVB12, VC Water-Soluble Vitamins are Soluble in water (Vitamins B and C) Used as helpers by many enzymes ( coenzymes ). VB3 VB11 ?VB9 , pantothenic acid VB7 , folic acid , Not stored in the body -get extra are urinated out

  4. 2- Fat-Soluble Vitamins A, D, E, and K. Soluble in lipids, but not in water. Important in vision, bone formation, antioxidants, and blood clotting. Stored in the body.

  5. Water soluble vitamins (B complex and vit C) Thiamin (Vitamin B1) Active form : Thiamin pyrophosphate TPP The first discovery of vitamin Deficiency results in beriberi (fatigue, weight loss, and nerve degeneration).

  6. Deficiency VB1beriberi

  7. Riboflavin (Vitamin B2) is Needed for good vision and healthy skin. Niacin (Vitamin B3) Deficiency can results in a condition known as pellagra. Pellagra includes the triad of 3D :dermatitis, dementia, and diarrhea. Is found in meats, rice, and whole grains Pantothenic Acid (Vitamin B5) needed for energy production as well as making glucose and cholesterol. Deficiency can result in fatigue, retarded growth, cramps, and anemia. Is found in salmon, meat, eggs, whole grains, and vegetables.

  8. Pyridoxine (Vitamin B6) Deficiency - Anemia - Skin problems - Sores in the mouth Cobalamin (Vitamin B12) Is a coenzyme for enzymes that transfer methyl groups and produce red blood cells. Deficiency can lead to megaloblastic anemia and nerve damage

  9. Ascorbic Acid (Vitamin C) Is required to make collagen Deficiency can lead to weakened connective tissue, slow-healing wounds, anemia and scurvy. Is found in blueberries, citrus fruits, tomatoes, broccoli, red and green vegetables.

  10. Fat soluble vitamins ( A, D, E, K ) Vitamin A is obtained from meats and beta-carotenes in plants (carrots for example) Beta-carotenes are converted by liver enzymes to vitamin A (retinol) which is mportant in vision, bone growth, and healthy skin Vitamin E Is an antioxidant in cells. Is found in vegetable oils, whole grains, and vegetables.

  11. Vitamin K is needed for activation of blood clotting factors so its deficiency associated with bleeding . Vitamin D (D3) Is synthesized in skin exposed to sunlight. Regulates the absorption of phosphorus and calcium during bone growth. Deficiency can result in weakened bones. Sources include egg yolk, and milk.

  12. Deficiency of vit D: rickets in children osteomalacia in adults

  13. GOOD LUCK

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