Transfinite inductionTransfinite induction is an extension of mathematical induction to well-ordered sets, for example to sets of ordinal numbers or cardinal numbers. Its correctness is a theorem of ZFC. Let be a property defined for all ordinals . Suppose that whenever is true for all , then is also true. Then transfinite induction tells us that is true for all ordinals. Usually the proof is broken down into three cases: Zero case: Prove that is true. Successor case: Prove that for any successor ordinal , follows from (and, if necessary, for all ).
AromaticityIn chemistry, aromaticity means the molecule has cyclic (ring-shaped) structures with pi bonds in resonance (those containing delocalized electrons). Aromatic rings give increased stability compared to saturated compounds having single bonds, and other geometric or connective non-cyclic arrangements with the same set of atoms. Aromatic rings are very stable and do not break apart easily. Organic compounds that are not aromatic are classified as aliphatic compounds—they might be cyclic, but only aromatic rings have enhanced stability.
In vivoStudies that are in vivo (Latin for "within the living"; often not italicized in English) are those in which the effects of various biological entities are tested on whole, living organisms or cells, usually animals, including humans, and plants, as opposed to a tissue extract or dead organism. This is not to be confused with experiments done in vitro ("within the glass"), i.e., in a laboratory environment using test tubes, Petri dishes, etc.
HepatocyteA hepatocyte is a cell of the main parenchymal tissue of the liver. Hepatocytes make up 80% of the liver's mass. These cells are involved in: Protein synthesis Protein storage Transformation of carbohydrates Synthesis of cholesterol, bile salts and phospholipids Detoxification, modification, and excretion of exogenous and endogenous substances Initiation of formation and secretion of bile The typical hepatocyte is cubical with sides of 20-30 μm, (in comparison, a human hair has a diameter of 17 to 180 μm).
Stem cellIn multicellular organisms, stem cells are undifferentiated or partially differentiated cells that can differentiate into various types of cells and proliferate indefinitely to produce more of the same stem cell. They are the earliest type of cell in a cell lineage. They are found in both embryonic and adult organisms, but they have slightly different properties in each. They are usually distinguished from progenitor cells, which cannot divide indefinitely, and precursor or blast cells, which are usually committed to differentiating into one cell type.
Freshwater fishFreshwater fish are those that spend some or all of their lives in fresh water, such as rivers and lakes, with a salinity of less than 1.05%. These environments differ from marine conditions in many ways, especially the difference in levels of salinity. To survive fresh water, the fish need a range of physiological adaptations. 41.24% of all known species of fish are found in fresh water. This is primarily due to the rapid speciation that the scattered habitats make possible.
Model organismA model organism (often shortened to model) is a non-human species that is extensively studied to understand particular biological phenomena, with the expectation that discoveries made in the model organism will provide insight into the workings of other organisms. Model organisms are widely used to research human disease when human experimentation would be unfeasible or unethical. This strategy is made possible by the common descent of all living organisms, and the conservation of metabolic and developmental pathways and genetic material over the course of evolution.
Fish anatomyFish anatomy is the study of the form or morphology of fish. It can be contrasted with fish physiology, which is the study of how the component parts of fish function together in the living fish. In practice, fish anatomy and fish physiology complement each other, the former dealing with the structure of a fish, its organs or component parts and how they are put together, such as might be observed on the dissecting table or under the microscope, and the latter dealing with how those components function together in living fish.
FishA fish (: fish or fishes) is an aquatic, craniate, gill-bearing animal that lacks limbs with digits. Included in this definition are the living hagfish, lampreys, and cartilaginous and bony fish as well as various extinct related groups. Approximately 95% of living fish species are ray-finned fish, belonging to the class Actinopterygii, with around 99% of those being teleosts. The earliest organisms that can be classified as fish were soft-bodied chordates that first appeared during the Cambrian period.
DNA repairDNA repair is a collection of processes by which a cell identifies and corrects damage to the DNA molecules that encode its genome. In human cells, both normal metabolic activities and environmental factors such as radiation can cause DNA damage, resulting in tens of thousands of individual molecular lesions per cell per day. Many of these lesions cause structural damage to the DNA molecule and can alter or eliminate the cell's ability to transcribe the gene that the affected DNA encodes.
In vitro fertilisationIn vitro fertilisation (IVF) is a process of fertilisation where an egg is combined with sperm in vitro ("in glass"). The process involves monitoring and stimulating a woman's ovulatory process, removing an ovum or ova (egg or eggs) from her ovaries and letting sperm fertilise them in a culture medium in a laboratory. After the fertilised egg (zygote) undergoes embryo culture for 2–6 days, it is transferred by catheter into the uterus, with the intention of establishing a successful pregnancy.
Mathematical inductionMathematical induction is a method for proving that a statement is true for every natural number , that is, that the infinitely many cases all hold. Informal metaphors help to explain this technique, such as falling dominoes or climbing a ladder: Mathematical induction proves that we can climb as high as we like on a ladder, by proving that we can climb onto the bottom rung (the basis) and that from each rung we can climb up to the next one (the step). A proof by induction consists of two cases.
