|
|
| Line 1: |
Line 1: |
| {{About|intervals of real numbers and other totally ordered sets|the most general definition|partially ordered set|other uses|Interval (disambiguation)}}
| | Doing home improvement by yourself, without professional help, can save a lot of money. Some projects can be done by novices as long as the novice knows what he or she is doing. This article is designed to help you do just that. When improving your house, take the neighborhood's character into consideration. A house that has a style completely different from those surrounding it may be problematic. A home that blends into the neighborhood will be easier to sell if you should decide to move. |
|
| |
|
| In [[mathematics]], a ('''real''') '''interval''' is a [[set (mathematics)|set]] of [[real number]]s with the property that any number that lies between two numbers in the set is also included in the set. For example, the set of all numbers {{mvar|x}} satisfying {{math|0 ≤ ''x'' ≤ 1}} is an interval which contains {{math|0}} and {{math|1}}, as well as all numbers between them. Other examples of intervals are the set of all real numbers <math>\R</math>, the set of all negative real numbers, and the [[empty set]].
| | If your kitchen's counter space is very limited, look into over-the-range microwaves. These microwave ovens are installed where the range hood normally goes. They offer various features, including convection cooking, and prices range widely. These units contain a recirculating ventilation system. Use aluminum foil to mask electrical outlets before painting your room. Aluminum foil is a lot easier to use than tape, and it will protect the covers from unintentional splatters. |
|
| |
|
| Real intervals play an important role in the theory of [[Integral|integration]], because they are the simplest sets whose "size" or "measure" or "length" is easy to define. The concept of measure can then be extended to more complicated sets of real numbers, leading to the [[Borel measure]] and eventually to the [[Lebesgue measure]].
| | It is quick and easy to remove, too. Make sure your paint is fully dry before removing the foil. Use a straight wall mounted coat rack to display your necklaces and bracelets. It is important to keep your valuable jewelry out of sight and only hang jewelry on the rack that is not of the highest value. Your signature pieces of jewelry can add a personal touch to your room's decor and also keep your necklaces and bracelets tangle free. |
|
| |
|
| Intervals are central to [[interval arithmetic]], a general [[numerical method|numerical computing]] technique that automatically provides guaranteed enclosures for arbitrary formulas, even in the presence of uncertainties, mathematical approximations, and [[rounding error|arithmetic roundoff]].
| | Choose pieces you wear frequently and keep them where you can reach them. Before beginning any home improvement project, find the locations of your gas shut-off. It is critical that you take extreme caution in these types of repairs. If you don't heed our warning, a fire or injury will likely be the result. Before starting any major landscaping project, make certain the new style will complement everything about your house. |
|
| |
|
| Intervals are likewise defined on an arbitrary [[total order|totally ordered]] set, such as [[integers]] or [[rational numbers]]. The notation of integer intervals is considered [[#Integer intervals|in the special section below]].
| | Matching styles between your home and landscape will improve the look and quality of your home, something that is impossible with clashing styles. Two PVC pipes can be easily attached using primer and cement made If you have any concerns concerning where and how to make use of home makeover ideas ([http://www.homeimprovementdaily.com simply click the following internet site]), you can contact us at our web page. for PVC. Without these items, the pipes won't stay together and liquids may leak from them. The surfaces of the pipes should also be water-free. Try to paint as a first step in any project. Painting the walls and ceiling of a room can be done far easier if you do it before having new flooring installed. |
|
| |
|
| ==Notations for intervals==
| | No matter what steps you take to protect your new floor, some paint is sure to find its way onto it. Do some floor refinishing to up your home's value. Although this can be a large job, it really isn't all that hard. You can find the proper equipment and maybe even classes at a hardware store near you. Performing this project will save you thousands over putting in a new floor. If you want to spruce up your home in a jiffy, replace the paneling on your walls. Not only is this a fast and cheap method of making your home nicer, but you can remove the panels if you are not pleased with how they look. |
| The interval of numbers between {{mvar|a}} and {{mvar|b}}, including {{mvar|a}} and {{mvar|b}}, is often denoted {{closed-closed|''a'', ''b''}}. The two numbers are called the ''endpoints'' of the interval. In countries where numbers are written with a [[decimal comma]], a [[semicolon]] may be used as a separator, to avoid ambiguity.
| |
| | |
| ===Excluding the endpoints===
| |
| To indicate that one of the endpoints is to be excluded from the set, the corresponding square bracket can be either replaced with a parenthesis, or reversed. Both notations are described in [[International standard]] [[ISO 31-11]]. Thus, in [[set builder notation]],
| |
| : <math> \begin{align}
| |
| (a,b) = \mathopen{]}a,b\mathclose{[} &= \{x\in\R\,|\,a<x<b\}, \\{}
| |
| [a,b) = \mathopen{[}a,b\mathclose{[} &= \{x\in\R\,|\,a\le x<b\}, \\{}
| |
| (a,b] = \mathopen{]}a,b\mathclose{]} &= \{x\in\R\,|\,a<x\le b\}, \\{}
| |
| [a,b] = \mathopen{[}a,b\mathclose{]} &= \{x\in\R\,|\,a\le x\le b\}.
| |
| \end{align} </math>
| |
| Note that {{open-open|''a'', ''a''}}, {{closed-open|''a'', ''a''}}, and {{open-closed|''a'', ''a''}} represent the [[empty set]], whereas {{closed-closed|''a'', ''a''}} denotes the set {{math|{''a''} }}. When {{math|''a'' > ''b''}}, all four notations are usually assumed to represent the empty set.
| |
| | |
| Both notations may overlap with other uses of parentheses and brackets in mathematics. For instance, the notation <math>(a,b)</math> is often used to denote an [[tuple|ordered pair]] in set theory, the [[coordinates]] of a [[point (geometry)|point]] or [[vector (mathematics)|vector]] in [[analytic geometry]] and [[linear algebra]], or (sometimes) a [[complex number]] in [[algebra]]. The notation <math>[a,b]</math> too is occasionally used for ordered pairs, especially in [[computer science]].
| |
| | |
| Some authors use <math>]a,b[</math> to denote the complement of the interval {{open-open|''a'', ''b''}}; namely, the set of all real numbers that are either less than or equal to {{mvar|a}}, or greater than or equal to {{mvar|b}}.
| |
| | |
| ===Infinite endpoints===
| |
| In both styles of notation, one may use an [[infinity (mathematics)|infinite]] endpoint to indicate that there is no bound in that direction. Specifically, one may use <math>a=-\infty</math> or <math>b=+\infty</math> (or both). For example, {{open-open|0, +∞}} is the set of all positive real numbers, and {{open-open|−∞, +∞}} is the set of real numbers.
| |
| | |
| The notations {{closed-closed|−∞, ''b''}} , {{closed-open|−∞, ''b''}} , {{closed-closed|''a'', +∞}} , and {{open-closed|''a'', +∞}} are ambiguous. For authors who define intervals as subsets of the real numbers, those notations are either meaningless, or equivalent to the open variants. In the latter case, the interval comprising all real numbers is both open and closed, {{open-open|−∞, +∞}} = {{closed-closed|−∞, +∞}} = {{closed-open|−∞, +∞}} = {{open-closed|−∞, +∞}} .
| |
| | |
| On the [[extended real number line]] the intervals are all different as this includes {{math|−∞}} and {{math|+∞}} elements. For example {{open-closed|−∞, +∞}} means the extended real numbers excluding only {{math|−∞}}.
| |
| | |
| The notation {{closed-closed|''a'' .. ''b''}} when {{mvar|a}} and {{mvar|b}} are [[integer]]s, or {{math|{''a'' .. ''b''} }}, or just {{math|''a'' .. ''b''}} is sometimes used to indicate the interval of all ''integers'' between {{mvar|a}} and {{mvar|b}}, including both. This notation is used in some [[programming language]]s; in [[Pascal programming language|Pascal]], for example, it is used to formally define a subrange type, most frequently used to specify lower and upper bounds of valid [[Indexed family|indices]] of an [[Array data type|array]].
| |
| | |
| An integer interval that has a finite lower or upper endpoint always includes that endpoint. Therefore, the exclusion of endpoints can be explicitly denoted by writing {{math|''a'' .. ''b'' − 1}} , {{math|''a'' + 1 .. ''b''}} , or {{math|''a'' + 1 .. ''b'' − 1}}. Alternate-bracket notations like {{closed-open|''a'' .. ''b''}} or {{math|[''a'' .. ''b''[}} are rarely used for integer intervals.
| |
| | |
| ==Terminology==
| |
| An '''open interval''' does not include its endpoints, and is indicated with parentheses. For example {{open-open|0,1}} means greater than {{math|0}} and less than {{math|1}}. A '''closed interval''' includes its endpoints, and is denoted with square brackets. For example {{closed-closed|0,1}} means greater than or equal to {{math|0}} and less than or equal to {{math|1}}.
| |
| | |
| A '''degenerate interval''' is any [[singleton set|set consisting of a single real number]]. Some authors include the empty set in this definition. A real interval that is neither empty nor degenerate is said to be '''proper''', and has infinitely many elements.
| |
| | |
| An interval is said to be '''left-bounded''' or '''right-bounded''' if there is some real number that is, respectively, smaller than or larger than all its elements. An interval is said to be '''bounded''' if it is both left- and right-bounded; and is said to be '''unbounded''' otherwise. Intervals that are bounded at only one end are said to be '''half-bounded'''. The empty set is bounded, and the set of all reals is the only interval that is unbounded at both ends. Bounded intervals are also commonly known as '''finite intervals'''.
| |
| | |
| Bounded intervals are [[bounded set]]s, in the sense that their [[diameter]] (which is equal to the [[absolute difference]] between the endpoints) is finite. The diameter may be called the '''length''', '''width''', '''measure''', or '''size''' of the interval. The size of unbounded intervals is usually defined as {{math|+∞}}, and the size of the empty interval may be defined as {{math|0}} or left undefined.
| |
| | |
| The '''centre''' ([[midpoint]]) of bounded interval with endpoints {{mvar|a}} and {{mvar|b}} is {{math|(''a'' + ''b'')/2}}, and its '''radius''' is the half-length {{math|{{mabs|''a'' − ''b''}}/2}}. These concepts are undefined for empty or unbounded intervals.
| |
| | |
| An interval is said to be '''left-open''' if and only if it has no [[minimum]] (an element that is smaller than all other elements); '''right-open''' if it has no [[maximum]]; and '''open''' if it has both properties. The interval {{closed-open|0,1}} = {{mset|''x'' | 0 ≤ ''x'' < 1}}, for example, is left-closed and right-open. The empty set and the set of all reals are open intervals, while the set of non-negative reals, for example, is a right-open but not left-open interval. The open intervals coincide with the [[open set]]s of the real line in its standard [[point-set topology|topology]].
| |
| | |
| An interval is said to be '''left-closed''' if it has a minimum element, '''right-closed''' if it has a maximum, and simply '''closed''' if it has both. These definitions are usually extended to include the empty set and to the (left- or right-) unbounded intervals, so that the closed intervals coincide with [[closed set]]s in that topology.
| |
| | |
| The '''interior''' of an interval {{mvar|I}} is the largest open interval that is contained in {{mvar|I}}; it is also the set of points in {{mvar|I}} which are not endpoints of {{mvar|I}}. The '''closure''' of {{mvar|I}} is the smallest closed interval that contains {{mvar|I}}; which is also the set {{mvar|I}} augmented with its finite endpoints.
| |
| | |
| For any set {{mvar|X}} of real numbers, the '''interval enclosure''' or '''interval span''' of {{mvar|X}} is the unique interval that contains {{mvar|X}} and does not properly contain any other interval that also contains {{mvar|X}}.
| |
| | |
| ==Classification of intervals==
| |
| The intervals of real numbers can be classified into eleven different types, listed below; where {{mvar|a}} and {{mvar|b}} are real numbers, with <math>a < b</math>:
| |
| | |
| : empty: <math>[b,a] = (a,a) = [a,a) = (a,a] = \{ \} = \emptyset</math>
| |
| : degenerate: <math>[a,a] = \{a\}</math>
| |
| : proper and bounded:
| |
| :: open: <math>(a,b)=\{x\,|\,a<x<b\}</math>
| |
| :: closed: <math>[a,b]=\{x\,|\,a\leq x\leq b\}</math>
| |
| :: left-closed, right-open: <math>[a,b)=\{x\,|\,a\,\leq x<b\}</math>
| |
| :: left-open, right-closed: <math>(a,b]=\{x\,|\,a<x\leq b\}</math>
| |
| : left-bounded and right-unbounded:
| |
| :: left-open: <math>(a,\infty)=\{x\,|\,x>a\}</math>
| |
| :: left-closed: <math>[a,\infty)=\{x\,|\,x\geq a\}</math>
| |
| : left-unbounded and right-bounded:
| |
| :: right-open: <math>(-\infty,b)=\{x\,|\,x<b\}</math>
| |
| :: right-closed: <math>(-\infty,b]=\{x\,|\,x\leq b\}</math>
| |
| : unbounded at both ends: <math>(-\infty,+\infty)=\R</math>
| |
| | |
| ===Intervals of the extended real line===
| |
| In some contexts, an interval may be defined as a subset of the [[extended real number line|extended real numbers]], the set of all real numbers augmented with {{math|−∞}} and {{math|+∞}}.
| |
| | |
| In this interpretation, the notations {{closed-closed|−∞, ''b''}} , {{closed-open|−∞, ''b''}} , {{closed-closed|''a'', +∞}} , and {{open-closed|''a'', +∞}} are all meaningful and distinct. In particular, {{open-open|−∞, +∞}} denotes the set of all ordinary real numbers, while {{closed-closed|−∞, +∞}} denotes the extended reals.
| |
| | |
| This choice affects some of the above definitions and terminology. For instance, the interval {{open-open|−∞, +∞}} = <math>\R</math> is closed in the realm of ordinary reals, but not in the realm of the extended reals.
| |
| | |
| ==Properties of intervals==
| |
| The intervals are precisely the [[connectedness|connected]] subsets of <math>\R</math>. It follows that the image of an interval by any [[continuous function (topology)|continuous]] function is also an interval. This is one formulation of the [[intermediate value theorem]].
| |
| | |
| The intervals are also the [[convex set|convex subset]]s of <math>\R</math>. The interval enclosure of a subset <math>X\subseteq \R</math> is also the [[convex hull]] of <math>X</math>.
| |
| | |
| The intersection of any collection of intervals is always an interval. The union of two intervals is an interval if and only if they have a non-empty intersection or an open end-point of one interval is a closed end-point of the other (e.g., <math>(a,b) \cup [b,c] = (a,c]</math>).
| |
| | |
| If <math>\R</math> is viewed as a [[metric space]], its [[open ball]]s are the open bounded sets {{open-open|''c'' + ''r'', ''c'' − ''r''}}, and its [[closed ball]]s are the closed bounded sets {{closed-closed|''c'' + ''r'', ''c'' − ''r''}}. | |
| | |
| Any element {{mvar|x}} of an interval {{mvar|I}} defines a partition of {{mvar|I}} into three disjoint intervals {{mvar|I}}<sub>1</sub>, {{mvar|I}}<sub>2</sub>, {{mvar|I}}<sub>3</sub>: respectively, the elements of {{mvar|I}} that are less than {{mvar|x}}, the singleton <math>[x,x] = \{x\}</math>, and the elements that are greater than {{mvar|x}}. The parts {{mvar|I}}<sub>1</sub> and {{mvar|I}}<sub>3</sub> are both non-empty (and have non-empty interiors) if and only if {{mvar|x}} is in the interior of {{mvar|I}}. This is an interval version of the [[trichotomy (mathematics)|trichotomy principle]].
| |
| | |
| ==Dyadic intervals==
| |
| | |
| A ''dyadic interval'' is a bounded real interval whose endpoints are <math>\frac{j}{2^n}</math> and <math>\frac{j+1}{2^n}</math>, where <math>j</math> and <math>n</math> are integers. Depending on the context, either endpoint may or may not be included in the interval.
| |
| | |
| Dyadic intervals have some nice properties, such as the following:
| |
| | |
| * The length of a dyadic interval is always an integer power of two.
| |
| * Every dyadic interval is contained in exactly one "parent" dyadic interval of twice the length.
| |
| * Every dyadic interval is spanned by two "child" dyadic intervals of half the length.
| |
| * If two open dyadic intervals overlap, then one of them must be a subset of the other.
| |
| | |
| The dyadic intervals thus have a structure very similar to an infinite [[binary tree]].
| |
| | |
| Dyadic intervals are relevant to several areas of numerical analysis, including [[adaptive mesh refinement]], [[multigrid methods]] and [[wavelet|wavelet analysis]]. Another way to represent such a structure is [[p-adic analysis]] (for {{mvar|p}}=2).<ref>{{cite journal |last1=Kozyrev |first1=Sergey |year=2002 |title=Wavelet theory as {{mvar|p}}-adic spectral analysis |journal=[[Izvestiya: Mathematics|Izvestiya RAN. Ser. Mat.]] |volume=66 |issue=2 |pages=149–158 |doi=10.1070/IM2002v066n02ABEH000381 |url=http://mi.mathnet.ru/eng/izv/v66/i2/p149 |accessdate=2012-04-05}}</ref>
| |
| | |
| == Generalizations ==
| |
| === Multi-dimensional intervals ===
| |
| In many contexts, an '''<math>n</math>-dimensional interval''' is defined as a subset of <math>\R^n</math> that is the [[Cartesian product]] of <math>n</math> intervals, <math>I = I_1\times I_2 \times \cdots \times I_n</math>, one on each [[coordinate]] axis.
| |
| | |
| For <math>n=2</math>, this generally defines a [[rectangle]] whose sides are parallel to the coordinate axes; for <math>n=3</math>, it defines an axis-aligned rectangular box.
| |
| | |
| A '''facet''' of such an interval <math>I</math> is the result of replacing any non-degenerate interval factor <math>I_k</math> by a degenerate interval consisting of a finite endpoint of <math>I_k</math>. The '''faces''' of <math>I</math> comprise <math>I</math> itself and all faces of its facets. The '''corners''' of <math>I</math> are the faces that consist of a single point of <math>\R^n</math>.
| |
| | |
| ===Complex intervals===
| |
| Intervals of [[complex number]]s can be defined as regions of the [[complex plane]], either [[rectangle|rectangular]] or [[disk (mathematics)|circular]].<ref>[http://books.google.com/books?id=Vtqk6WgttzcC Complex interval arithmetic and its applications], Miodrag Petković, Ljiljana Petković, Wiley-VCH, 1998, ISBN 978-3-527-40134-5</ref>
| |
| | |
| ==Topological algebra==
| |
| Intervals can be associated with points of the plane and hence regions of intervals can be associated with [[region (mathematical analysis)|region]]s of the plane. Generally, an interval in mathematics corresponds to an ordered pair (''x,y'') taken from the [[direct product]] R × R of real numbers with itself. Often it is assumed that ''y'' > ''x''. For purposes of [[mathematical structure]], this restriction is discarded,<ref>Kaj Madsen (1979) [http://www.ams.org/mathscinet/pdf/586220.pdf Review of "Interval analysis in the extended interval space" by Edgar Kaucher] from [[Mathematical Reviews]]</ref> and "reversed intervals" where ''y'' − ''x'' < 0 are allowed. Then the collection of all intervals [''x,y''] can be identified with the [[topological ring]] formed by the [[direct sum of modules#Direct sum of algebras|direct sum]] of R with itself where addition and multiplication are defined component-wise.
| |
| | |
| The direct sum algebra <math>( R \oplus R, +, \times)</math> has two [[ideal (ring theory)|ideal]]s, { [''x'',0] : ''x'' ∈ R } and { [0,''y''] : ''y'' ∈ R }. The [[identity element]] of this algebra is the condensed interval [1,1]. If interval [''x,y''] is not in one of the ideals, then it has [[multiplicative inverse]] [1/''x'', 1/''y'']. Endowed with the usual [[topology]], the algebra of intervals forms a [[topological ring]]. The [[group of units]] of this ring consists of four [[quadrant (plane geometry)|quadrant]]s determined by the axes, or ideals in this case. The [[identity component]] of this group is quadrant I.
| |
| | |
| Every interval can be considered a symmetric interval around its [[midpoint]]. In a reconfiguration published in 1956 by M Warmus, the axis of "balanced intervals" [''x'', −''x''] is used along with the axis of intervals [''x,x''] that reduce to a point.
| |
| Instead of the direct sum <math>R \oplus R</math>, the ring of intervals has been identified<ref>[[D. H. Lehmer]] (1956) [http://www.ams.org/mathscinet/pdf/81372.pdf Review of "Calculus of Approximations"] from Mathematical Reviews</ref> with the [[split-complex number]] plane by M. Warmus and [[D. H. Lehmer]] through the identification
| |
| : ''z'' = (''x'' + ''y'')/2 + j (''x'' − ''y'')/2.
| |
| This linear mapping of the plane, which amounts of a [[ring isomorphism]], provides the plane with a multiplicative structure having some analogies to ordinary complex arithmetic, such as [[polar decomposition#Alternative planar decompositions|polar decomposition]].
| |
| | |
| ==See also==
| |
| *[[Inequality (mathematics)|Inequality]]
| |
| *[[Interval arithmetic]]
| |
| *[[Interval graph]]
| |
| *[[Interval finite element]]
| |
| | |
| ==References==
| |
| {{reflist}}
| |
| | |
| * T. Sunaga, [http://www.cs.utep.edu/interval-comp/sunaga.pdf "Theory of interval algebra and its application to numerical analysis"], In: Research Association of Applied Geometry (RAAG) Memoirs, Ggujutsu Bunken Fukuy-kai. Tokyo, Japan, 1958, Vol. 2, pp. 29-46 (547-564); reprinted in Japan Journal on Industrial and Applied Mathematics, 2009, Vol. 26, No. 2-3, pp. 126-143.
| |
| | |
| ==External links==
| |
| * ''A Lucid Interval'' by Brian Hayes: An [http://www.americanscientist.org/issues/pub/a-lucid-interval American Scientist article] provides an introduction.
| |
| *[http://id.mind.net/~zona/mmts/miscellaneousMath/intervalNotation/intervalNotation.html Interval Notation Basics]
| |
| *[http://www.cs.utep.edu/interval-comp/main.html Interval computations website]
| |
| *[http://www.cs.utep.edu/interval-comp/icompwww.html Interval computations research centers]
| |
| * [http://demonstrations.wolfram.com/IntervalNotation/ Interval Notation] by George Beck, [[Wolfram Demonstrations Project]].
| |
| * {{MathWorld |title=Interval |urlname=Interval}}
| |
| | |
| {{DEFAULTSORT:Interval (Mathematics)}}
| |
| [[Category:Sets of real numbers]]
| |
| [[Category:Order theory]]
| |
| [[Category:Topology]]
| |
Doing home improvement by yourself, without professional help, can save a lot of money. Some projects can be done by novices as long as the novice knows what he or she is doing. This article is designed to help you do just that. When improving your house, take the neighborhood's character into consideration. A house that has a style completely different from those surrounding it may be problematic. A home that blends into the neighborhood will be easier to sell if you should decide to move.
If your kitchen's counter space is very limited, look into over-the-range microwaves. These microwave ovens are installed where the range hood normally goes. They offer various features, including convection cooking, and prices range widely. These units contain a recirculating ventilation system. Use aluminum foil to mask electrical outlets before painting your room. Aluminum foil is a lot easier to use than tape, and it will protect the covers from unintentional splatters.
It is quick and easy to remove, too. Make sure your paint is fully dry before removing the foil. Use a straight wall mounted coat rack to display your necklaces and bracelets. It is important to keep your valuable jewelry out of sight and only hang jewelry on the rack that is not of the highest value. Your signature pieces of jewelry can add a personal touch to your room's decor and also keep your necklaces and bracelets tangle free.
Choose pieces you wear frequently and keep them where you can reach them. Before beginning any home improvement project, find the locations of your gas shut-off. It is critical that you take extreme caution in these types of repairs. If you don't heed our warning, a fire or injury will likely be the result. Before starting any major landscaping project, make certain the new style will complement everything about your house.
Matching styles between your home and landscape will improve the look and quality of your home, something that is impossible with clashing styles. Two PVC pipes can be easily attached using primer and cement made If you have any concerns concerning where and how to make use of home makeover ideas (simply click the following internet site), you can contact us at our web page. for PVC. Without these items, the pipes won't stay together and liquids may leak from them. The surfaces of the pipes should also be water-free. Try to paint as a first step in any project. Painting the walls and ceiling of a room can be done far easier if you do it before having new flooring installed.
No matter what steps you take to protect your new floor, some paint is sure to find its way onto it. Do some floor refinishing to up your home's value. Although this can be a large job, it really isn't all that hard. You can find the proper equipment and maybe even classes at a hardware store near you. Performing this project will save you thousands over putting in a new floor. If you want to spruce up your home in a jiffy, replace the paneling on your walls. Not only is this a fast and cheap method of making your home nicer, but you can remove the panels if you are not pleased with how they look.