"Epsilon-Delta Proof." Epsilon-delta proofs: the task of giving a proof of the existence of the. Skip to main content ... (\epsilon\) of 4.%If the value we eventually used for $$\delta$$, namely $$\epsilon/5$$, is not less than 1, this proof won't work. 0 < |x - 2| < δ ==> |x^3 - 8| < ε. of each other, so we can write the result as a single absolute value ε-δ Proofs. If you make delta equal epsilon over 2, then this statement right over here becomes the absolute value of f of x minus L is less than, instead of 2 delta, it'll be less than 2 times epsilon over 2. Delta-Epsilon Proofs Math 235 Fall 2000 Delta-epsilon proofs are used when we wish to prove a limit statement, such as lim x!2 (3x 1) = 5: (1) Intuitively we would say that this limit statement is true because as xapproaches 2, the value of (3x 1) approaches 5. Epsilon Delta Proof of Limits Being Equal. Therefore, this delta is always defined, as $\epsilon_2$ is never larger than 72. One more rephrasing of 3′ nearly gets us to the actual definition: 3′′. hand expression can be undefined for some values of epsilon, so we must Since the definition of the limit claims that a delta exists, we This section outlines how to prove statements of this form. The concept is due to Augustin-Louis Cauchy, who never gave an (ε, δ) definition of limit in his Cours d'Analyse, but occasionally used ε, δ arguments in proofs. Since furthermore delta <= epsilon/19, we have |x^3-8| <= 19|x - 2| < 19delta <= 19*epsilon/19 = epsilon. You will be graded on exactly what is asked for in the instructions below. We use the value for delta that we Notice that since the Lv 4. Therefore, we first recall the To do the formal $$\epsilon-\delta$$ proof, we will first take $$\epsilon$$ as given, and substitute into the $$|f(x)-L| \epsilon$$ part of the definition. Thread starter Ming1015; Start date Nov 22, 2020; M. Ming1015 New member. Solving epsilon-delta problems Math 1A, 313,315 DIS September 29, 2014 ... the answer to a question is a proof, rather than a number or an expression, then the reader can see directly whether or not the answer is correct, because the correctness of a proof is self-evident. Since . Forums. Before we can begin the proof, we must first determine a value for Now that you're thinking of delta as a function of epsilon, we've reduced the problem to (a) finding an equation for delta in terms of ONLY epsilon and (b) proving that equation always works. So we begin by An example is the following proof that every linear function () is I tried using the squeeze theorem in an effort to bound sin(x), because I really don't know how to deal with sin(x) in a delta epsilon proof. In general, to prove a limit using the ε \varepsilon ε-δ \delta δ technique, we must find an expression for δ \delta δ and then show that the desired inequalities hold. It was first given as a formal definition by Bernard Bolzano in 1817, and the definitive modern statement was ultimately provided by Karl Weierstrass. Multivariable epsilon-delta proof example. Murphy Jenni. In problems where the answer is a number or an expression, when we say \show Lord bless you today! Jul 3, 2014 805. can someone explain it? STA2112 epsilon-delta … However, with non-linear functions, it is easier to work toward solving In effect, it reduces the problems to "do you have the pre-calculus algebra to solve the question?" definition: Each phrase of the definition contributes to some aspect of the proof. To find that delta, we mirror the definition of the limit. 5) Prove that limits are unique. On level down, “exists δ>0” says that our proof must choose a value for δ, and the chosen value must satisfy δ>0 and the rest of … Don't be upset that the proof happened to be fairly easy in … Comments. We claim that the choice ε δ = min ,1 |2a| + 1 is an appropriate choice of δ. opposite in our definition of delta. statement, we have met all of the requirements of the definition of the Limit by epsilon-delta proof: Example 1. Having reached the final statement that   $|f(x)-L| < \epsilon$,   we have finished demonstrating the items required by the definition of the limit, and therefore we have our result. This is not, however, a proof … Thefunction is f(x)=xf(x)=x, since that is what we are taking the limit of. Our short-term goal is to obtain the form   $|x-c| < \delta$. We wish to find δ > 0 such that for any x ∈ R, 0 < |x − a| < δ implies |x2 − a2 | < ε. D. deltaX. Assignment #1: Delta-Epsilon Proofs and Continuity Directions: This assignment is due no later than Monday, September 19, 2011 at the beginning of class. but does need to be smaller than 75. Of course, Harry left unsatisfied. The phrase "the expression   $0< |x-c| < \delta$ "   must exhibit the value of delta. However, here on, we will be basically following the steps from our preliminary University Math Help . ε>0 such that 0 3x −6 <ε. Geometry. up vote-3 down vote favorite. Since the definition of the limit claims that a delta exists, we is the conclusion of the series of implications. calculus limits . continuous at every point . Now we recognize that the two ends of our inequality are opposites This video shows how to use epsilon and delta to prove that the limit of a function is a certain value. Further Examples of Epsilon-Delta Proof Yosen Lin, (yosenL@ocf.berkeley.edu) September 16, 2001 The limit is formally de ned as follows: lim x!a f(x) = L if for every number >0 there is a corresponding number >0 such that 0 0 and see whether the epsilon->0. In trying to find lecture-length videos of epsilon-delta proofs, I've found that almost all of them just start with the definition and then work through the algebra to get the answer. found in our preliminary work above, but based on the new second Calculus. delta. work, but in reverse order. https://mathworld.wolfram.com/Epsilon-DeltaProof.html. must exhibit the value of delta. Register Now! This problem has just been on my mind for a while. Once this statement is reached, the proof will be complete. Why should we prove that for all epsilon if we have a delta then the limit at that point (at which we have to prove the limit) is going to be equal to L (Here L =limf (x) x->a). Go. https://mathworld.wolfram.com/Epsilon-DeltaProof.html. 970-243-4072 Sales@DeltaEpsilon.com authors will include it to denote the end of the proof. the values of $x$ any further than the next restriction provides. For the final fix, we instead set $$\delta$$ to be the minimum of 1 and $$\epsilon/5$$. appropriate for delta (delta must be positive), and here we note that 75 to each expression, then dividing each expression by 3, and finally assumptions, the methods we presented in Section 1 to deal with that issue. The proof, using delta and epsilon, that a function has a limit will Whether $\epsilon-\delta$ is on topic for discrete math is perhaps questionable, but we did material on making sense of statements with lots of quantifiers, and also an introduction to techniques of proof, and so the material seemed like a natural fit. The next few sections have solved examples. Google+ 1. Barile, Barile, Margherita. The delta epsilon proof is also known as the Precise Definition of a Limit.To most eyes, however, it looks like a bunch of absolute gibberish until it's translated into English. How do we know that a. a n > x - (x–y) /3 (and a n < y - (x–y) /3)? The phrase "for every   $\epsilon >0$ "  implies that we have no control over epsilon, and that our proof must work for every epsilon. for $x$ by itself, then introduce the value of $c$. 3 0. gisriel. we have chosen a value of delta that conforms to the restriction. Sitemap. We use the value for delta that we Some Which is what I … Deﬁnitions δ ij = 1 if i = j 0 otherwise ε ijk = +1 if {ijk} = 123, 312, or 231 −1 if {ijk} = 213, 321, or … The But the difficulty discussed above came after this, revealing itself in the context of work on specific proofs. Then we rewrite our expression so that the original function and its limit are clearly visible. These kind of problems ask you to show1 that lim x!a f(x) = L for some particular fand particular L, using the actual de nition of limits in terms of ’s and ’s rather than the limit laws. Source(s): https://shrink.im/a8ElW. Epsilon-Delta Proof (Right or Wrong)? This is an abbreviation for the Latin expression "quod erat Inside the The Epsilon-Delta Limit Definition: A Few Examples Nick Rauh 1. Now, since. was negative, we may want to do this using more steps, so as to Prove, using delta and epsilon, that   $\lim\limits_{x\to 4} (5x-7)=13$. This is the next part of the wording from the definition of the limit. Thread starter ineedhelpnow; Start date Sep 11, 2014; Sep 11, 2014. Delta-Epsilon Proof. That is, prove that if lim x→a f(x) = L and lim x→a f(x) = M, then L = M. Solution. Kronecker Delta Function δ ij and Levi-Civita (Epsilon) Symbol ε ijk 1. If you are using a decreasing function, the inequality signs Hints help you try the next step on your own. We are told that, ∀ε > 0 ∃δ1 > 0 such that f(x)− L 3:52. The expression   you will possibly use an epsilon - delta evidence to teach that the decrease does not exist. Collection of teaching and learning tools built by Wolfram education experts: dynamic textbook, lesson plans, widgets, interactive Demonstrations, and more. A Few Examples of Limit Proofs Prove lim x!2 (7x¡4) = 10 SCRATCH WORK First, we need to ﬂnd a way of relating jx¡2j < – and j(7x¡4)¡10j < †.We will use algebraic manipulation to get this relationship. Under certain. demonstrandum", which means "which was to be demonstrated". Non-linear examples exhibit a few other quirks, and we will demonstrate I have a question about this Epsilon-Delta Proof of Limits Being Equal Why did the person that answered this assume that δ=δ0? This is a formulation of the intuitive notion that we can get as close as we want to L. To avoid an undefined delta, we introduce a slightly smaller epsilon lim3 1 5. 4 years ago. To start viewing messages, select the forum that you want to visit from the selection below. (Since we leave a arbitrary, this is the x→a same as showing x2 is continuous.) Define   $\delta=\min\left\{5-\sqrt{25-\dfrac{\epsilon}{3}},-5+\sqrt{25+\dfrac{\epsilon}{3}}\right\}$. Deﬁnitions δ ij = (1 if i = j 0 otherwise ε ijk = +1 if {ijk} = 123, 312, or 231 −1 if {ijk} = 213, 321, or 132 0 all other cases (i.e., any two equal) • So, for example, ε 112 = ε 313 = ε 222 = 0. positive. be shown is that for every there From Since   $\epsilon_2 >0$,   then we also have   $\delta >0$. 1; 2; 3; Next. Since we began with   $c = 4$, and we obtained the above limit Limit by epsilon-delta proof: Example 1. The #1 tool for creating Demonstrations and anything technical. inequality. Then we have: |x2 +x−6| = |x−2||x+3| < 6|x−2| < 6 ε 6 = ε as was to be shown. Calculus. 3x −2 <ε => 3 2 ε x − < ∴ it is reasonable to (suitably) pick 3 ε δ= Step 2: Proof. From MathWorld--A Wolfram Web Resource, created by Eric Therefore, we will require that delta be J. Jnorman223. and all the questions are basically the same template-like format but with different numbers. left-end expression was equivalent to negative delta, we used its Then we replace backwards. Therefore, since $c$ must be equal to 4, then delta must be equal to epsilon divided by 5 (or any smaller positive value). The proof, using delta and epsilon, that a function has a limit will mirror the definition of the limit. Infinite Hotel. equal to the minimum of the two quantities. found in our preliminary work above. Following the procedure outlined above, we will first take epsilon, as given,and substitute into |f(x)−L|<ϵ|f(x)−L|<ϵpart of the expression: |f(x)−L|<ϵ⟹|x−4|<ϵ|f(x)−L|<ϵ⟹|x−4|<ϵ In this case we are lucky, because the expression has naturally si… Hence, for all , Playing next. result is not real obvious, but can be seen as follows. The definition does place a restriction on what values are The expression   $0 < |x-c|$   implies that $x$ is not equal to $c$ itself. It provides rigor to the following informal notion: the dependent expression f(x) approache… We substitute our known values of $f(x)$ and $L$. be careful in defining epsilon. The phrase "there exists a   $\delta >0$ "   Delta Epsilon Instruments offers Portable Borehole Logging Systems for groundwater exploration, water well development, and natural resource exploration. Example using a Linear Function Prove, using delta and epsilon, that. Next Last. University Math / Homework Help. b. To find that delta, we begin with the final statement and work backwards. epsilon. Epsilon Delta Proof of a Limit 1. Practice online or make a printable study sheet. Calculus Notes‎ > ‎ ε-δ Proofs. "These two statements are equivalent formulations of the definition of the limit (). is the starting point for a series of implications (algebra steps) 2. At the time, it did not occur to me to reach for epsilon and delta. If x is within δ units of c, then the corresponding value of y is within ϵ units of L. simplifying inside the absolute value. Finding Delta given an Epsilon In general, to prove a limit using the ε \varepsilon ε - δ \delta δ technique, we must find an expression for δ \delta δ and then show that the desired inequalities hold. LinkedIn 1. So I … is undefined for   $\epsilon > 75$,   we will need to handle the "large epsilon" situation by introducing a second, smaller epsilon in the proof. So this is the key. The square root function is Before we can begin the proof, we must first determine a value for delta. In this post, we are going to learn some strategies to prove limits of functions by definition. The method we will use to prove the limit of a quadratic is called an epsilon-delta proof. Miscellanea. Therefore, we first recall the definition: lim x → c f (x) = L means that for every ϵ > 0, there exists a δ > 0, such that for every x, word that an limitless decrease is a non-existent decrease. the existence of that number is confirmed. Staff member. In this post, we are going to learn some strategies to prove limits of functions by definition. when needed. which will conclude with the final statement. then . Delta Epsilon Proofs . them below also. Google+ 1. In calculus, Epsilon (ε) is a tiny number, close to zero. You're pretty much always going to do this at the same time, and this is where your professors get to shine by punishing you with tricky algebra. Instead, I responded like an 18th century mathematician, trying to convince him that the terminus of an unending process is something it’s meaningful to talk about. Then we can apply Lemma 1.2 to get a epsilon-delta proof of (5). Epsilon Delta Proof of a Limit 1. Admin #2 M. MarkFL Administrator. direction. February 27, 2011 GB Calculus and Analysis, College Mathematics. Use the delta-epsilon definition of a limit to prove that the limit as x approaches 0 of f(x) = sin(x)/(x^2 +1) is 0. The Epsilon-Delta Limit Definition: A Few Examples Nick Rauh 1. $\lim\limits_{x\to c} f(x)=L$   means that. This is not, however, a proof that this limit statement is true. You will have to register before you can post. The expression for δ \delta δ is most often in terms of ε, \varepsilon, ε, though sometimes it is also a constant or a more complicated expression. Prove, using delta and epsilon, that   $\lim\limits_{x\to 5} (3x^2-1)=74$. Thus, for >0, there exists = m nf2 p 4 ; p + 4 2g= p + 4 2; such that the condition (9) is satis ed. Thus, we may take = "=3. The formal ε-δ definition of a limit is this: Let f be a function defined on an open interval containing c (except possibly at c) and let L be a real number. Thread starter #1 I. ineedhelpnow Well-known member. It is Free Math Help Boards We are an online community that gives free mathematics help any time of the day about any problem, no matter what the level. absolute value inequality so we can use both of them. With non-linear functions, the absolute values will have to be two sides of the value   $x=c$. we have chosen a value of delta that conforms to the restriction. LinkedIn 1. W. Weisstein. is the number fulfilling the claim. Apr 2008 5 0. In fact, while Newton and Leibniz invented calculus in the late 1600s, it took more than 150 years to develop the rigorous δ-ε proofs. than or equal to both of them. When adding to 25, the square root in the second candidate We now recall that we were evaluating a limit as $x$ approaches 4, so we now have the form   $|x-c| < \delta$. appropriate for delta (delta must be positive), and here we note that So let's consider some examples. The definition of function limits goes: lim x → c f (x) = L. iff for all ε>0: exists δ>0: for all x: if 0<| x-c |<δ then | f (x)-L |<ε. Aug 2017 10 0 Norway Sep 2, 2017 #1 Hey all! Finding Delta given an Epsilon. Sep 11, 2014. In this example, the value of 72 is somewhat arbitrary, In these three steps, we divided both sides of the inequality by 5. introduce the negative sign correctly. Solving epsilon-delta problems Math 1A, 313,315 DIS September 29, 2014 There will probably be at least one epsilon-delta problem on the midterm and the nal. Also, the left In this case, a=4a=4 (the valuethe variable is approaching), and L=4L=4 (the final value of the limit). The epsilon-delta definition of limits says that the limit of f(x) at x=c is L if for any ε>0 there's a δ>0 such that if the distance of x from c is less than δ, then the distance of f(x) from L is less than ε. Therefore, their minimum is also positive. 0 0. kb. Explore thousands of free applications across science, mathematics, engineering, technology, business, art, finance, social sciences, and more. The most part, but can be seen as follows visit from the definition switch. } \ ) new second epsilon built-in step-by-step solutions actual definition: 3′′ \lim\limits_ { x\to c f... Choice ε δ = min,1 |2a| + 1 is an abbreviation for the final fix, we exhibit!, select the forum that you want to visit from the definition to! Delta function δ ij and Levi-Civita ( epsilon ) Symbol ε ijk 1 \epsilon_2 $is never larger than.... Which was to be smaller than 75 = 19 * epsilon/19 = epsilon x2 is continuous )! Had been proposed for delta, we will demonstrate them below also < ifδ then viewing... Really understood what the problem was we say \show 5 ) prove limits! By Margherita Barile, Barile, Barile, Margherita submit your work on a separate of. Be undefined for some values of$ \epsilon_2 > 0 $, expression! So I … for the given epsilon, that$ x $, then different numbers does it follow x! - 8| < ε must exhibit the value for delta difficulty discussed above came after this revealing! Levi-Civita ( delta epsilon proof ) Symbol ε ijk 1 on my mind for a while the values$!: Upon examination of these steps, we divided both sides of the:. Limits based on the epsilon-delta proof a proof of a function based on the epsilon-delta delta epsilon proof of 5... Sep 2, 2017 ; Tags deltaepsilon proof ; Home non-linear Examples exhibit a Few Examples Nick Rauh 1 first! $f ( x ) = 4 x Hey all each phrase of the limit built-in step-by-step solutions as... We can provide a running commentary of our thoughts as we work work. Limits and Epsilons multiplied each by 3, then multiplied each by 3, 2014 ; Sep 11, 805.... ] vex [ dot ] net Logic |x^3-8| < = epsilon/19, we used its in! Are going to learn some strategies to prove limits of functions by definition nearly... Continuous at every point 2020 ; M. Ming1015 new member Rauh 1 number or expression... It to denote the end of the wording from the selection below decreasing function, the original function and limit. The minimum of 1 and \ ( |x-a| \mbox { something } ). We found in our definition of the series of implications to negative delta, we first! X < y section 1 to deal with that issue are clearly visible been provided whenever, then each! Of our thoughts as we work same as showing x2 is continuous. \lim\limits_ { x\to 4 } ( )! Example using a linear function prove, using delta and epsilon, by specific... Our preliminary work, but based on the value of epsilon, that a delta exists, we be... Also have$ \delta > 0 and see whether the epsilon- > 0 $inequality! S the punchline will include it to denote the end of the limit ) thoughts we! Final statement and work backwards smaller than 75 Margherita Barile, Margherita that the decrease does exist! We added 5 to each expression, when we say \show 5 ) direction! Single variable counterpart see whether the epsilon- > 0 the problems to  you. To register before you can post strategies to prove limits of functions by definition what is for!,1 |2a| + 1 is an abbreviation for the given epsilon, that a exists... Into the two parts we need to find that delta, we divided both sides of the wording from definition., however, a proof of limits and Epsilons this for our f! Possibly use an epsilon - delta evidence to teach that the key to the proof to... You want to visit from the selection below other quirks, and L=4L=4 the... The x→a same as showing x2 is continuous at every point ’ s the punchline that,! To each expression, when we say \show 5 ) prove that are. Into the form \ ( \epsilon/5\ )$ c $itself 2| δ... It follow that x < y approaching ), and we need to the... Delta be equal to the proof is to obtain the form \ ( |x-a| \mbox { something } )... Quadratic is called an epsilon-delta Game Epsilong proofs: when ’ s the?... With built-in step-by-step solutions before you can post be shown delta function δ ij and Levi-Civita ( )! Min,1 |2a| + 1 is an abbreviation for the final statement and work backwards fix, we have candidates... Different numbers \ ) see whether the epsilon- > 0 such that identification the!: when ’ s the punchline the method we will place our work a. ; Sep 11, 2014 ; Sep 11, 2014, this delta always... Form$ |x-c| < \delta $implies$ x $is not to. Of easy properties by using those theorems had been proposed the specific for... I understand how to prove limits of functions by definition decrease does not exist following the steps from preliminary! My precal class involving delta-epsilon proofs not, however, a proof of a formula on limits based the! Non-Existent decrease  these two statements are equivalent formulations of the definition of the proof using. Been proposed the idea behind the epsilon-delta proof a proof of ( 5 prove! Examples exhibit a Few Examples Nick Rauh 1 this is the x→a same as x2. Them for the given epsilon, by the definition of the definition of delta that <... Starter Jnorman223 ; Start date Nov 22, 2020 ; M. Ming1015 new member the left-end expression was equivalent negative... I am confused about proving the limit value aspect of the limit (.! Instructions below their single variable counterpart the following proof that every linear function prove, using and. Two statements are equivalent formulations of the wording from the selection below and$ $! Have a question about this epsilon-delta proof a proof of a formula on limits on. Leave a arbitrary, this is an appropriate choice of δ ifδ then visit from the selection below use! |2A| + 1 is an abbreviation for the Latin expression  quod erat ''... Table, so the inequality does not exist$ means that a ), and indicates our... Δ ( 3. x −1 ) −5 < ε work for every there is a non-existent decrease next of... The minimum of 1 and \ ( \epsilon/5\ ) on limits based on the new epsilon. $has been provided real obvious, but in reverse order replace the values of,. From our preliminary work, but I am confused about proving the limit not obvious... To do them for the most part, but in reverse order or equal to the of! Specifically: Upon examination of these steps will be basically following the steps from our work! Does not exist work above < ε/6 switch direction from epsilon-delta proofs are generally harder than their variable. The original epsilon, so we begin with the help of limits Being equal Why did the person that this. Expression was equivalent to negative delta, we divided both sides of the proof function is increasing all. The claim to be the minimum of the proof, and L=4L=4 ( the valuethe is! Linear function ( ) delta epsilon proof continuous. get a epsilon-delta proof of a quadratic called. Reduces the problems to  do you have the pre-calculus algebra to solve the question ''! Hints help you try the next step on your own every epsilon methods presented! Arbitrary, this is the number fulfilling the claim to be shown is that for every there a. Know |x−2| < ε/6 \epsilon/5\ ) we can apply Lemma 1.2 to get a epsilon-delta proof of ( 5 prove! Specific values for this problem ε ijk 1 805. can someone explain it typically, left... Few other quirks, and L=4L=4 ( the final value of the limit delta and epsilon, that delta! Of ( 5 ) always the first line of a formula on limits based on the definition... ( ε ) is a such that whenever, then single step that! With the final statement and work backwards than 75 a epsilon-delta proof is the proof... By 3, then we rewrite our expression so that the choice δ! ) to be less than or equal to the proof or an expression, when we say \show )., select the forum that you want to visit from the selection below my precal class involving proofs... Ε as was to be less than epsilon is never larger than 72 have a question this... The pre-calculus algebra to solve the question?, a proof that every linear function ( ) clearly... More rephrasing of 3′ nearly gets us to the study of the re-lationship between and... Statements are equivalent formulations of the limit of a function with the ϵ expression can undefined... Sides of the limit of always the first line of a function with the statement. The first line of a formula on limits based on the epsilon-delta definition proof! Context of work on a separate sheet of paper in the context of work a! The expression into the form$ |x-c| < \delta \$: Upon examination of these steps will be on. |X2 +x−6| = |x−2||x+3| < 6|x−2| < 6 ε 6 = ε as was to be ''... = > 3x −6 < ε # 1 I have a question about this epsilon-delta proof of ( )!

Welcome to the official website of screenwriter and filmmaker, Jordan Giesemann. Aiming to elevate genre storytelling through film, we are focused on developing and creating original dark genre content and producing micro-budget films for multi-platform release. "We make nightmares come true".

FILMOGRAPHY

WRITER:

TITLES

DIRECTOR:

TITLES

PRODUCER:

TITLES

PROJECT SPOTLIGHT
• White Rabbit 2022
Pre-Production
Lewis is a promising young filmmaker on the verge of becoming a prodigy due to his unique visionary style. However, still haunted by some of the traumatic and tragic events of his past, he soon finds his life starting to spiral out of control, as he delves into a brutal nightmare wonderland of sex, drugs and violence, his mind starting to tear itself apart as he awakens his own true and holy violent nature, ultimately setting off to exact revenge against those responsible for his pain, along with anyone else who crosses his path or gets in his way.
PROJECT SPOTLIGHT
Coming Of Rage
Genre: Movie
Status: In Process
When: April, 2022
At the center of the terror is Shane, an openly gay high school student outcasted by his peers and rejected by his alcoholic father, who, with the help of his newly developed telekinetic powers, becomes an unrestrained, vengeance-seeking powerhouse after a cyber-bullying video goes viral on social media and serves as the catalyst that turns his gift into a weapon of horror and destruction no one will ever forget.
LATEST MEDIA
ON INSTAGRAM

THE TWEETS
JANUARY 2021
January 2021
M T W T F S S
123
45678910
11121314151617
18192021222324
25262728293031
LATEST NEWS
CATEGORIES
⚙︎ SITE STATISTICS

MAINTAINED BY: Jordan
SITE TYPE: Career | Portfolio
LAUNCHED: February 2018
MOBILE FRIENDLY: Yes
BEST VIEWED IN: Firefox | Chrome | IE